Publications HAL

2023

titre
Kawasaki dynamics beyond the uniqueness threshold
auteur
Roland Bauerschmidt, Thierry Bodineau, Benoît Dagallier
article
2023
resume
Glauber dynamics of the Ising model on a random regular graph is known to mix fast below the tree uniqueness threshold and exponentially slowly above it. We show that Kawasaki dynamics of the canonical ferromagnetic Ising model on a random $d$-regular graph mixes fast beyond the tree uniqueness threshold when $d$ is large enough (and conjecture that it mixes fast up to the tree reconstruction threshold for all $d\geq 3$). This result follows from a more general spectral condition for (modified) log-Sobolev inequalities for conservative dynamics of Ising models. The proof of this condition in fact extends to perturbations of distributions with log-concave generating polynomial.
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https://hal.science/hal-04236370/file/rrg.pdf BibTex
titre
Stochastic dynamics and the Polchinski equation: an introduction
auteur
Roland Bauerschmidt, Thierry Bodineau, Benoît Dagallier
article
2023
resume
This introduction surveys a renormalisation group perspective on log-Sobolev inequalities and related properties of stochastic dynamics. We also explain the relationship of this approach to related recent and less recent developments such as Eldan's stochastic localisation and the Föllmer process, the Boué--Dupuis variational formula and the Barashkov--Gubinelli approach, the transportation of measure perspective, and the classical analogues of these ideas for Hamilton--Jacobi equations which arise in mean-field limits.
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https://hal.science/hal-04163695/file/intro.pdf BibTex
titre
Dynamics Of Dilute Gases At Equilibrium: From The Atomistic Description To Fluctuating Hydrodynamics
auteur
Thierry Bodineau, Isabelle Gallagher, Laure Saint-Raymond, Sergio Simonella
article
Annales Henri Poincaré, 2023, Proceedings of ICM 2022, ⟨10.1007/s00023-022-01257-y⟩
resume
We derive linear fluctuating hydrodynamics as the low density limit of a deterministic system of particles at equilibrium. The proof builds upon previous results of the authors where the asymptotics of the covariance of the fluctuation field is obtained, and on the proof of the Wick rule for the fluctuation field.
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https://hal.science/hal-03822200/file/Fluctuations_hydro_14-10-2022.pdf BibTex

2022

titre
Large deviations for out of equilibrium correlations in the symmetric simple exclusion process
auteur
Thierry Bodineau, Benoit Dagallier
article
2022
resume
For finite size Markov chains, the Donsker-Varadhan theory fully describes the large deviations of the time averaged empirical measure. We are interested in the extension of the Donsker-Varadhan theory for a large size non-equilibrium system: the one-dimensional symmetric simple exclusion process connected with reservoirs at different densities. The Donsker-Varadhan functional encodes a variety of scales depending on the observable of interest. In this paper, we focus on the time-averaged two point correlations and investigate the large deviations from the steady state behaviour. To control two point correlations out of equilibrium, the key input is the construction of a simple approximation to the invariant measure. This approximation is quantitative in time and space as estimated through relative entropy bounds building on the work of Jara and Menezes arXiv:1810.09526.
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https://hal.science/hal-03912965/file/Correlations_final_2022_21_12.pdf BibTex
titre
Statistical dynamics of a hard sphere gas: fluctuating Boltzmann equation and large deviations
auteur
Thierry Bodineau, Isabelle Gallagher, Laure Saint-Raymond, Sergio Simonella
article
2022
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https://hal.science/hal-02920308/file/BGSRS_main.pdf BibTex
titre
Cluster expansion for a dilute hard sphere gas dynamics
auteur
Thierry Bodineau, Isabelle Gallagher, Laure Saint-Raymond, Sergio Simonella
article
Proceedings of the International Congress on Mathematical Physics, special issue of Journal of Mathematical Physics, 2022, 63, ⟨10.1063/5.0091199⟩
resume
In [7], a cluster expansion method has been developed to study the fluctuations of the hard sphere dynamics around the Boltzmann equation. This method provides a precise control on the exponential moments of the empirical measure, from which the fluctuating Boltzmann equation and large deviation estimates have been deduced. The cluster expansion in [7] was implemented at the level of the BBGKY hierarchy, which is a standard tool to investigate the deterministic dynamics [11]. In this paper, we introduce an alternative approach, in which the cluster expansion is applied directly on real trajectories of the particle system. This offers a fresh perspective on the study of the hard sphere dynamics in the low density limit, allowing to recover the results obtained in [7], and also to describe the actual clustering of particle trajectories.
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https://hal.science/hal-03661646/file/BGSRS_dce.pdf BibTex
titre
Dynamics of dilute gases : a statistical approach
auteur
Thierry Bodineau, Isabelle Gallagher, Laure Saint-Raymond, Sergio Simonella
article
2022
resume
The evolution of a gas can be described by different models depending on the observation scale. A natural question, raised by Hilbert in his sixth problem, is whether these models provide consistent predictions. In particular, for rarefied gases, it is expected that continuum laws of kinetic theory can be obtained directly from molecular dynamics governed by the fundamental principles of mechanics. In the case of hard sphere gases, Lanford showed that the Boltzmann equation emerges as the law of large numbers in the low density limit, at least for very short times. The goal of this survey is to present recent progress in the understanding of this limiting process, providing a complete statistical description.
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https://hal.science/hal-03540993/file/HAL-ICM-BGSS-3-3-2022.pdf BibTex
titre
Long-time derivation at equilibrium of the fluctuating Boltzmann equation
auteur
Thierry Bodineau, Isabelle Gallagher, Laure Saint-Raymond, Sergio Simonella
article
2022
resume
We study a hard sphere gas at equilibrium, and prove that in the low density limit, the fluctuations converge to a Gaussian process governed by the fluctuating Boltzmann equation. This result holds for arbitrarily long times. The method of proof builds upon the weak convergence method introduced in the companion paper [8] which is improved by considering clusters of pseudo-trajectories as in [7].
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https://hal.science/hal-03519557/file/Duhamel-7-1-2022.pdf BibTex

2021

titre
Log-Sobolev Inequality for the Continuum Sine-Gordon Model
auteur
Roland Bauerschmidt, Thierry Bodineau
article
Commun.Pure Appl.Math., 2021, 74 (10), pp.2064-2113. ⟨10.1002/cpa.21926⟩
resume
We derive a multiscale generalisation of the Bakry-Émery criterion for a measure to satisfy a log-Sobolev inequality. Our criterion relies on the control of an associated PDE well-known in renormalisation theory: the Polchinski equation. It implies the usual Bakry-Émery criterion, but we show that it remains effective for measures that are far from log-concave. Indeed, using our criterion, we prove that the massive continuum sine-Gordon model with β < 6π satisfies asymptotically optimal log-Sobolev inequalities for Glauber and Kawasaki dynamics. These dynamics can be seen as singular SPDEs recently constructed via regularity structures, but our results are independent of this theory. © 2021 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC.
Accès au bibtex
https://arxiv.org/pdf/1907.12308 BibTex
titre
Long-Time Correlations For A Hard-Sphere Gas At Equilibrium
auteur
Thierry Bodineau, Isabelle Gallagher, Laure Saint-Raymond, Sergio Simonella
article
Communications on Pure and Applied Mathematics, In press, ⟨10.48550/arXiv.2012.03813⟩
resume
It has been known since Lanford [22] that the dynamics of a hard sphere gas is described in the low density limit by the Boltzmann equation, at least for short times. The classical strategy of proof fails for longer times, even close to equilibrium. In this paper, we introduce a weak convergence method coupled with a sampling argument to prove that the covariance of the fluctuation field around equilibrium is governed by the linearized Boltzmann equation globally in time (including in diffusive regimes). This method is much more robust and simple than the one devised in [4] which was specific to the 2D case.
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https://hal.science/hal-03041164/file/fluctuationL2-2revised-october-28.pdf BibTex

2020

titre
Fluctuation theory in the Boltzmann--Grad limit
auteur
Thierry Bodineau, Isabelle Gallagher, Laure Saint-Raymond, Sergio Simonella
article
Journal of Statistical Physics, 2020, 180, pp.873-895
resume
We develop a rigorous theory of hard-sphere dynamics in the kinetic regime, away from thermal equilibrium. In the low density limit, the empirical density obeys a law of large numbers and the dynamics is governed by the Boltzmann equation. Deviations from this behaviour are described by dynamical correlations, which can be fully characterized for short times. This provides both a fluctuating Boltzmann equation and large deviation asymptotics.
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https://hal.science/hal-02526608/file/hardsphere-dynamics%20statphys%2025.03.pdf BibTex

2019

titre
A microscopic view of the Fourier law
auteur
Thierry Bodineau, Isabelle Gallagher, Laure Saint-Raymond
article
Comptes Rendus. Physique, 2019, 20, pp.402 - 418. ⟨10.1016/j.crhy.2019.08.002⟩
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https://arxiv.org/pdf/1912.03947 BibTex
titre
Spectral gap critical exponent for Glauber dynamics of hierarchical spin models
auteur
Roland Bauerschmidt, Thierry Bodineau
article
Communications in Mathematical Physics, 2019, ⟨10.1007/s00220-019-03553-x⟩
resume
We develop a renormalisation group approach to deriving the asymptotics of the spectral gap of the generator of Glauber type dynamics of spin systems at and near a critical point. In our approach, we derive a spectral gap inequality, or more generally a Brascamp-Lieb inequality, for the measure recursively in terms of spectral gap or Brascamp-Lieb inequalities for a sequence of renormalised measures. We apply our method to hierarchical versions of the $4$-dimensional $n$-component $|\varphi|^4$ model at the critical point and its approach from the high temperature side, and the $2$-dimensional Sine-Gordon and the Discrete Gaussian models in the rough phase (Kosterlitz-Thouless phase). For these models, we show that the spectral gap decays polynomially like the spectral gap of the dynamics of a free field (with a logarithmic correction for the $|\varphi|^4$ model), the scaling limit of these models in equilibrium.
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https://arxiv.org/pdf/1809.02075 BibTex
titre
A very simple proof of the LSI for high temperature spin systems
auteur
Roland Bauerschmidt, Thierry Bodineau
article
Journal of Functional Analysis, 2019, 276 (8)
resume
We present a very simple proof that the $O(n)$ model satisfies a uniform logarithmic Sobolev inequality (LSI) if the positive definite coupling matrix has largest eigenvalue less than $n$. This condition applies in particular to the SK spin glass model at inverse temperature $\beta < 1/4$. It is the first result of rapid relaxation for the SK model and requires significant cancellations between the ferromagnetic and anti-ferromagnetic spin couplings that cannot be obtained by existing methods to prove Log-Sobolev inequalities. The proof also applies to more general bounded and unbounded spin systems. It uses a single step of zero range renormalisation and Bakry--Emery theory for the renormalised measure.
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https://arxiv.org/pdf/1712.03676 BibTex
titre
A MICROSCOPIC VIEW ON THE FOURIER LAW
auteur
Thierry Bodineau, Isabelle Gallagher, Laure Saint-Raymond
article
Comptes Rendus. Physique, 2019
resume
The Fourier law of heat conduction describes heat diffusion in macroscopic systems. This physical law has been experimentally tested for a large class of physical systems. A natural question is to know whether it can be derived from the microscopic models using the fundamental laws of mechanics.
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https://hal.science/hal-02390229/file/CRAS-Fourier_last.pdf BibTex

2018

titre
Exact Hydrodynamic Description of Active Lattice Gases
auteur
Mourtaza Kourbane-Houssene, Clément Erignoux, Thierry Bodineau, Julien Tailleur
article
Physical Review Letters, 2018, 120 (26), pp.268003. ⟨10.1103/PhysRevLett.120.268003⟩
resume
We introduce a class of lattice gas models of active matter systems whose hydrodynamic description can be derived exactly. We illustrate our approach by considering two systems exhibiting two of the most studied collective behaviours in active matter: the motility-induced phase separation and the transition to collective motion. In both cases, we derive coupled partial differential equation describing the dynamics of the local density and polarization fields and show how they quantitatively predict the emerging properties of the macroscopic lattice gases.
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https://hal.science/hal-01721363/file/1801.08952 BibTex
titre
Quantitative estimates for the flux of TASEP with dilute site disorder
auteur
Christophe Bahadoran, Thierry Bodineau
article
Electronic Journal of Probability, 2018, 23, ⟨10.1214/18-EJP137⟩
resume
We prove that the flux function of the totally asymmetric simple exclusion process (TASEP) with site disorder exhibits a flat segment for sufficiently dilute disorder. For high dilution, we obtain an accurate description of the flux. The result is established under a decay assumption of the maximum current in finite boxes, which is implied in particular by a sufficiently slow power tail assumption on the disorder distribution near its minimum. To circumvent the absence of explicit invariant measures, we use an original renormalization procedure and some ideas inspired by homogenization.
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https://hal.science/hal-01275166/file/Plateau__04_12_17.pdf BibTex
titre
One-sided convergence in the Boltzmann-Grad limit
auteur
Thierry Bodineau, Isabelle Gallagher, Laure Saint-Raymond, Sergio Simonella
article
Annales de la Faculté des Sciences de Toulouse. Mathématiques., 2018, 27 (5), ⟨10.5802/afst.1589⟩
resume
We review various contributions on the fundamental work of Lanford deriving the Boltzmann equation from hard-sphere dynamics in the low density limit. We focus especially on the assumptions made on the initial data and on how they encode irreversibility. The impossibility to reverse time in the Boltzmann equation (expressed for instance by Boltzmann's H-theorem) is related to the lack of convergence of higher order marginals on some singular sets. Explicit counterexamples single out the microscopic sets where the initial data should converge in order to produce the Boltzmann dynamics.
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https://hal.science/hal-01413299/file/Irreversibility13.pdf BibTex
titre
Derivation of an ornstein-uhlenbeck process for a massive particle in a rarified gas of particles
auteur
Thierry Bodineau, Isabelle Gallagher, Laure Saint-Raymond
article
Annales de l'Institut Henri Poincare Physique Theorique, 2018, 19 (6), ⟨10.1007/s00023-018-0674-6⟩
resume
We consider the statistical motion of a convex rigid body in a gas of N smaller (spherical) atoms close to thermodynamic equilibrium. Because the rigid body is much bigger and heavier, it undergoes a lot of collisions leading to small deflections. We prove that its velocity is described, in a suitable limit, by an Ornstein-Uhlenbeck process. The strategy of proof relies on Lanford's arguments [17] together with the pruning procedure from [3] to reach diffusive times, much larger than the mean free time. Furthermore, we need to introduce a modified dynamics to avoid pathological collisions of atoms with the rigid body: these collisions, due to the geometry of the rigid body, require developing a new type of trajectory analysis.
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https://hal.science/hal-01609594/file/bigparticle.pdf BibTex

2017

titre
From Hard Sphere Dynamics to the Stokes–Fourier Equations: An Analysis of the Boltzmann–Grad Limit
auteur
Thierry Bodineau, Isabelle Gallagher, Laure Saint-Raymond
article
Annals of PDE, 2017, 3 (1), ⟨10.1007/s40818-016-0018-0⟩
resume
We derive the linear acoustic and Stokes-Fourier equations as the limiting dynamics of a system of N hard spheres of diameter $\epsilon$ in two space dimensions, when N $\rightarrow$ $\infty$, $\epsilon$ $\rightarrow$ 0, N $\epsilon$ = $\alpha$ $\rightarrow$ $\infty$, using the linearized Boltzmann equation as an intermediate step. Our proof is based on Lanford's strategy [18], and on the pruning procedure developed in [5] to improve the convergence time to all kinetic times with a quantitative control which allows us to reach also hydrodynamic time scales. The main novelty here is that uniform L 2 a pri-ori estimates combined with a subtle symmetry argument provide a weak version of chaos, in the form of a cumulant expansion describing the asymptotic decorrelation between the particles. A refined geometric analysis of recollisions is also required in order to discard the possibility of multiple recollisions.
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https://hal.science/hal-01226094/file/boltzlinearise_14_09_16.pdf BibTex

2015

titre
Interface Motion in Random Media
auteur
T. Bodineau, A. Teixeira
article
Communications in Mathematical Physics, 2015, 334 (2), pp.843 - 865. ⟨10.1007/s00220-014-2152-4⟩
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titre
THE BROWNIAN MOTION AS THE LIMIT OF A DETERMINISTIC SYSTEM OF HARD-SPHERES
auteur
Thierry Bodineau, Isabelle Gallagher, Laure Saint-Raymond
article
Inventiones Mathematicae, 2015, 41 p
resume
We provide a rigorous derivation of the brownian motion as the limit of a deterministic system of hard-spheres as the number of particles N goes to infinity and their diameter ε simultaneously goes to 0, in the fast relaxation limit α = N ε d−1 → ∞ (with a suitable diffusive scaling of the observation time). As suggested by Hilbert in his sixth problem, we rely on a kinetic formulation as an intermediate level of description between the microscopic and the fluid descriptions: we use indeed the linear Boltzmann equation to describe one tagged particle in a gas close to global equilibrium. Our proof is based on the fundamental ideas of Lanford. The main novelty here is the detailed study of the branching process, leading to explicit estimates on pathological collision trees.
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https://hal.science/hal-01137218/file/BGSR_revision_3.pdf BibTex

2014

titre
Lyapunov functionals for boundary-driven nonlinear drift-diffusions
auteur
T. Bodineau, J. L. Lebowitz, C. Mouhot, Cédric Villani
article
Nonlinearity, 2014, 27 (9), pp.2111--2132
resume
We exhibit a large class of Lyapunov functionals for nonlinear drift-diffusion equations with non-homogeneous Dirichlet boundary conditions. These are generalizations of large deviation functionals for underlying stochastic many-particle systems, the zero range process and the Ginzburg-Landau dynamics, which we describe briefly. As an application, we prove linear inequalities between such an entropy-like functional and its entropy production functional for the boundary-driven porous medium equation in a bounded domain with positive Dirichlet conditions: this implies exponential rates of relaxation related to the first Dirichlet eigenvalue of the domain. We also derive Lyapunov functions for systems of nonlinear diffusion equations, and for nonlinear Markov processes with non-reversible stationary measures.
Accès au bibtex
https://arxiv.org/pdf/1305.7405 BibTex

2013

titre
Universal current fluctuations in the symmetric exclusion process and other diffusive systems
auteur
Eric Akkermans, Thierry Bodineau, Bernard Derrida, Ohad Shpielberg
article
EPL - Europhysics Letters, 2013, 103 (2)
resume
We show, using the macroscopic fluctuation theory of Bertini, De Sole, Gabrielli, Jona-Lasinio, and Landim, that the statistics of the current of the symmetric simple exclusion process (SSEP) connected to two reservoirs are the same on an arbitrary large finite domain in dimension $d$ as in the one dimensional case. Numerical results on squares support this claim while results on cubes exhibit some discrepancy. We argue that the results of the macroscopic fluctuation theory should be recovered by increasing the size of the contacts. The generalization to other diffusive systems is straightforward.
Accès au bibtex
https://arxiv.org/pdf/1306.3145 BibTex

2012

titre
Finite size scaling of the dynamical free-energy in a kinetically constrained model
auteur
V. Lecomte, T. Bodineau, C. Toninelli
article
Journal of Statistical Physics, 2012, 147 (1), pp.1-17. ⟨10.1007/s10955-012-0458-1⟩
resume
We determine the finite size corrections to the large deviation function of the activity in a kinetically constrained model (the Fredrickson-Andersen model in one dimension), in the regime of dynamical phase coexistence. Numerical results agree with an effective model where the boundary between active and inactive regions is described by a Brownian interface.
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https://arxiv.org/pdf/1111.6394 BibTex
titre
Activity phase transition for constrained dynamics
auteur
Thierry Bodineau, Cristina Toninelli
article
Communications in Mathematical Physics, 2012, 311 (2), pp.357-396. ⟨10.1007/s00220-012-1449-4⟩
resume
We consider two cases of kinetically constrained models, namely East and FA-1f models. The object of interest of our work is the activity A(t) defined as the total number of configuration changes in the interval [0,t] for the dynamics on a finite domain. It has been shown in [GJLPDW1,GJLPDW2] that the large deviations of the activity exhibit a non-equilibirum phase transition in the thermodynamic limit and that reducing the activity is more likely than increasing it due to a blocking mechanism induced by the constraints. In this paper, we study the finite size effects around this first order phase transition and analyze the phase coexistence between the active and inactive dynamical phases in dimension 1. In higher dimensions, we show that the finite size effects are also determined by the dimension and the choice of boundary conditions.
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https://arxiv.org/pdf/1101.1760 BibTex

2011

titre
Phase fluctuations in the ABC model
auteur
Thierry Bodineau, Bernard Derrida
article
Journal of Statistical Physics, 2011, 145 (3), pp.745--762. ⟨10.1007/s10955-011-0315-7⟩
resume
We analyze the fluctuations of the steady state profiles in the modulated phase of the ABC model. For a system of $L$ sites, the steady state profiles move on a microscopic time scale of order $L^3$. The variance of their displacement is computed in terms of the macroscopic steady state profiles by using fluctuating hydrodynamics and large deviations. Our analytical prediction for this variance is confirmed by the results of numerical simulations.
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https://arxiv.org/pdf/1108.2039 BibTex

2010

titre
A diffusive system driven by a battery or by a smoothly varying field
auteur
Bernard Derrida, T. Bodineau, J. L. Lebowitz
article
Journal of Statistical Physics, 2010, 140 (4), pp.648-675. ⟨10.1007/s10955-010-0012-y⟩
resume
We consider the steady state of a one dimensional diffusive system, such as the symmetric simple exclusion process (SSEP) on a ring, driven by a battery at the origin or by a smoothly varying field along the ring. The battery appears as the limiting case of a smoothly varying field, when the field becomes a delta function at the origin. We find that in the scaling limit, the long range pair correlation functions of the system driven by a battery turn out to be very different from the ones known in the steady state of the SSEP maintained out of equilibrium by contact with two reservoirs, even when the steady state density profiles are identical in both models.
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2008

titre
Copolymers at selective interfaces: new bounds on the phase diagram
auteur
T. Bodineau, G. Giacomin, H. Lacoin, Fabio Lucio Toninelli
article
2008
resume
We investigate the phase diagram of disordered copolymers at the interface between two selective solvents, and in particular its weak-coupling behavior, encoded in the slope $m_c$ of the critical line at the origin. In mathematical terms, the partition function of such a model does not depend on all the details of the Markov chain that models the polymer, but only on the time elapsed between successive returns to zero and on whether the walk is in the upper or lower half plane between such returns. This observation leads to a natural generalization of the model, in terms of arbitrary laws of return times: the most interesting case being the one of return times with power law tails (with exponent $1+\ga$, $\ga=1/2$ in the case of the symmetric random walk). The main results we present here are: 1/ The improvement of the known result $1/(1+\alpha)\le m_c\le 1$, as soon as $\ga >1$ for what concerns the upper bound, and down to $\ga\approx 0.65$ for the lower bound. 2/ A proof of the fact that the critical curve lies strictly below the critical curve of the annealed model for every non-zero value of the coupling parameter. We also provide an argument that rigorously shows the strong dependence of the phase diagram on the details of the return probability (and not only on the tail behavior). Lower bounds are obtained by exhibiting a new localization strategy, while upper bounds are based on estimates of non-integer moments of the partition function.
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https://arxiv.org/pdf/0803.1766 BibTex
titre
Large deviations of lattice Hamiltonian dynamics coupled to stochastic thermostats
auteur
T. Bodineau, R. Lefevere
article
2008
resume
We discuss the Donsker-Varadhan theory of large deviations in the framework of Hamiltonian systems thermostated by a Gaussian stochastic coupling. We derive a general formula for the Donsker-Varadhan large deviation functional for dynamics which satisfy natural properties under time reversal. Next, we discuss the characterization of the stationary state as the solution of a variational principle and its relation to the minimum entropy production principle. Finally, we compute the large deviation functional of the current in the case of a harmonic chain thermostated by a Gaussian stochastic coupling.
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https://arxiv.org/pdf/0802.1104 BibTex
titre
Large deviations of lattice Hamiltonian dynamics coupled to stochastic thermostats
auteur
R. Lefevere, T. Bodineau
article
Journal of Statistical Physics, 2008, 133, pp.1-27
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titre
Copolymers at selective interfaces: new bounds on the phase diagram
auteur
G. Giacomin, T. Bodineau, H. Lacoin, F.L. Toninelli
article
Journal of Statistical Physics, 2008, 132 (4), pp.603-626
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titre
Long range correlations and phase transition in non-equilibrium diffusive systems
auteur
Bernard Derrida, T. Bodineau, V. Lecomte, F. Van Wijland
article
Journal of Statistical Physics, 2008, 133 (6), pp.1013-1031. ⟨10.1007/s10955-008-9647-3⟩
resume
We obtain explicit expressions for the long range correlations in the ABC model and in diffusive models conditioned to produce an atypical current of particles.In both cases, the two-point correlation functions allow to detect the occurrence of a phase transition as they become singular when the system approaches the transition.
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2006

titre
3D crystal: how flat its flat facets are?
auteur
T. Bodineau, R.H. Schonman, Senya Shlosman
article
Communications in Mathematical Physics, 2006, 255 n.3, pp.747-766
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titre
Current large deviations for Asymmetric Exclusion Processes with open boundaries
auteur
Thierry Bodineau, Bernard Derrida
article
Journal of Statistical Physics, 2006, 123 (2), pp.277--300
resume
We study the large deviation functional of the current for the Weakly Asymmetric Simple Exclusion Process in contact with two reservoirs. We compare this functional in the large drift limit to the one of the Totally Asymmetric Simple Exclusion Process, in particular to the Jensen-Varadhan functional. Conjectures for generalizing the Jensen-Varadhan functional to open systems are also stated.
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https://arxiv.org/pdf/cond-mat/0509179 BibTex
titre
Translation invariant Gibbs states for the Ising model
auteur
T. Bodineau
article
Probability Theory and Related Fields, 2006, 135 n.2, pp.153-168
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2005

titre
A universality property for last-passage percolation paths close to the axis
auteur
Thierry Bodineau, James Martin
article
Electronic Communications in Probability, 2005, 10, pp.105 - 112
resume
We consider a last-passage directed percolation model in $Z_+^2$, with i.i.d. weights whose common distribution has a finite $(2+p)$th moment. We study the fluctuations of the passage time from the origin to the point $(n,n^a)$. We show that, for suitable $a$ (depending on $p$), this quantity, appropriately scaled, converges in distribution as $n\to\infty$ to the Tracy-Widom distribution, irrespective of the underlying weight distribution. The argument uses a coupling to a Brownian directed percolation problem and the strong approximation of Komlós, Major and Tusnàdy.
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https://hal.science/hal-00003004/file/fluct5.pdf BibTex
titre
Slab percolation for the Ising model
auteur
T. Bodineau
article
Probability Theory and Related Fields, 2005, 132 n.1, pp.83-118
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titre
Distribution of current in non-equilibrium diffusive systems and phase transitions
auteur
T. Bodineau, B. Derrida
article
Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2005, 72, 066110, 8 p
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2004

titre
Translation invariant Gibbs states for the Ising model
auteur
Thierry Bodineau
article
2004
resume
We prove that all the translation invariant Gibbs states of the Ising model are a linear combination of the pure phases $\mu^+_\gb,\mu^-_\gb$ for any $\gb \not = \gb_c$. This implies that the average magnetization is continuous for $\gb >\gb_c$. Furthermore, combined with previous results on the slab percolation threshold this shows the validity of Pisztora's coarse graining up to the critical temperature.
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https://hal.science/hal-00003038/file/PMA-937.pdf BibTex
titre
Current fluctuations in non-equilibrium diffusive systems : an additivity principle
auteur
T. Bodineau, Bernard Derrida
article
Physical Review Letters, 2004, 92, ⟨10.1103/PhysRevLett.92.180601⟩
resume
We formulate a simple additivity principle allowing to calculate the whole distribution of current fluctuations through a large one dimensional system in contact with two reservoirs at unequal densities from the knowledge of its first two cumulants. This distribution (which in general is non-Gaussian) satisfies the Gallavotti-Cohen symmetry and generalizes the one predicted recently for the symmetric simple exclusion process. The additivity principle can be used to study more complex diffusive networks including loops.
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On the localization transition of random copolymers near selective interfaces
auteur
T. Bodineau, G. Giacomin
article
Journal of Statistical Physics, 2004, 117 n.5-6, pp.801-818
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titre
Current fluctuations in non-equilibrium diffusive systems: an additivity principle
auteur
T. Bodineau, B. Derrida
article
Physical Review Letters, 2004, 92 - 180601, pp.1-4
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From dynamic to static large deviations in boundary driven exclusion particle systems
auteur
T. Bodineau, G. Giacomin
article
Stochastic Processes and their Applications, 2004, 110 n.1, pp.67-81
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titre
Stability of interfaces and stochastic dynamics in the regime of partial wetting
auteur
T. Bodineau, D. Ioffe
article
Annales Henri Poincaré. A Journal of Theoretical and Mathematical Physics, 2004, 5 n.5, pp.871-914
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2003

titre
Surface tension and Wulff shape for a lattice model without spin flip symmetry
auteur
T. Bodineau, E. Presutti
article
Annales Henri Poincaré, 2003, 4 n.5, pp.847-896
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