PreprintCC BY 4.0arXiv
Non-equilibrium fluctuations of gradient exclusion processes in dimension d≤ 3
Abstract
We consider a gradient, speed-change, symmetric exclusion process on the discrete torus Tdn, d≤ 3, whose empirical measure evolves, on the diffusive scale, according to a non-linear parabolic equation. We prove that, starting from a sequence of initial states whose relative entropy with respect to the inhomogeneous product measure associated with the initial profile is o(nd/2), and whose density fluctuation field converges, the density fluctuation field converges, in L1(0,T; H− r), to the solution of a linear stochastic partial differential equation with time-dependent coefficients driven by a conservative space-time white noise.
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BibTeX
@misc{landim2026nonequilibrium,
title = {{Non-equilibrium fluctuations of gradient exclusion processes in dimension $d\le 3$}},
author = {Claudio Landim and Sunder Sethuraman},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37897},
eprint = {2609.37897},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37897},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Non-equilibrium fluctuations of gradient exclusion processes in dimension d≤ 3
AU - Claudio Landim
AU - Sunder Sethuraman
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37897
UR - https://arxiv.org/abs/2609.37897
AB - We consider a gradient, speed-change, symmetric exclusion process on the discrete torus T^d_n, d≤ 3, whose empirical measure evolves, on the diffusive scale, according to a non-linear parabolic equation. We prove that, starting from a sequence of initial states whose relative entropy with respect to the inhomogeneous product measure associated with the initial profile is o(n^d/2), and whose density fluctuation field converges, the density fluctuation field converges, in L^1(0,T; H_− r), to the solution of a linear stochastic partial differential equation with time-dependent coefficients driven by a conservative space-time white noise.
ER -