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Dynamical large deviations for boundary driven gradient symmetric exclusion processes in mild contact with reservoirs

A. Bouley, C. Landim

Abstract

We consider a one-dimensional gradient symmetric exclusion process in mild contact with boundary reservoirs. The hydrodynamic limit of the empirical measure is given by a non-linear second-order parabolic equation with non-linear Robin boundary conditions. We prove the dynamical large deviations principle.

Dynamical large deviations for boundary driven gradient symmetric exclusion processes in mild contact with reservoirs

Abstract

We consider a one-dimensional gradient symmetric exclusion process in mild contact with boundary reservoirs. The hydrodynamic limit of the empirical measure is given by a non-linear second-order parabolic equation with non-linear Robin boundary conditions. We prove the dynamical large deviations principle.
Paper Structure (8 sections, 35 theorems, 145 equations)

This paper contains 8 sections, 35 theorems, 145 equations.

Table of Contents

  1. Introduction
  2. Notation and results
  3. Hydrodynamic limit
  4. The rate function
  5. Deconstructing the rate functional
  6. $I_{[0,T]}(.|\gamma)$-density
  7. The large deviations principle
  8. Uniqueness of weak solutions

Key Result

Theorem 2.2

Fix $T>0$ and a profile $\rho_0\colon \Omega \to [0,1]$. Let $(\mu^N)_{N \in \mathbb{N}}$ be a sequence of measure on ${\mathfrak S}_N$ associated to $\rho_0$. Then, the sequence of probability measures $(\mathbb{Q}_{\mu^N}^N)_{N \in \mathbb{N}}$ converges weakly to the probability measure $\mathbb{

Theorems & Definitions (61)

  • Definition 2.1
  • Theorem 2.2
  • Definition 2.3
  • Theorem 2.4
  • Theorem 2.5
  • Remark 2.6
  • Definition 2.7
  • Definition 2.8
  • Proposition 2.9
  • Remark 2.10
  • ...and 51 more