PreprintarXiv licencearXiv
Equilibrium fluctuations of the weakly asymmetric inclusion process
Abstract
We prove that the stationary density fluctuation field of the one-dimensional weakly asymmetric simple inclusion process converges to the energy solution of the stochastic Burgers equation. The key technical ingredient is a second-order Boltzmann-Gibbs principle tailored to the microscopic current. As a consequence, we also obtain Ornstein-Uhlenbeck fluctuations for the symmetric inclusion process in a weakly condensing regime, a result of independent interest.
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BibTeX
@misc{gabriel2026equilibrium,
title = {{Equilibrium fluctuations of the weakly asymmetric inclusion process}},
author = {Simon Gabriel},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29957},
eprint = {2608.29957},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29957},
}
RIS
TY - UNPB
TI - Equilibrium fluctuations of the weakly asymmetric inclusion process
AU - Simon Gabriel
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.29957
UR - https://arxiv.org/abs/2608.29957
AB - We prove that the stationary density fluctuation field of the one-dimensional weakly asymmetric simple inclusion process converges to the energy solution of the stochastic Burgers equation. The key technical ingredient is a second-order Boltzmann-Gibbs principle tailored to the microscopic current. As a consequence, we also obtain Ornstein-Uhlenbeck fluctuations for the symmetric inclusion process in a weakly condensing regime, a result of independent interest.
ER -