Equilibrium fluctuations for the weakly asymmetric discrete Atlas model
Probability
2017-09-21 v1 Mathematical Physics
math.MP
Abstract
This contribution aims at presenting and generalizing a recent work of Hernandez, Jara and Valentim [DOI:10.1016/j.spa.2016.06.026]. We consider the weakly asymmetric version of the so-called discrete Atlas model, which has been introduced there. Precisely, we look at some equilibrium fluctuation field of a weakly asymmetric zero-range process which evolves on a discrete half-line, with a source of particles at the origin. We prove that its macroscopic evolution is governed by a stochastic heat equation with Neumann or Robin boundary conditions, depending on the range of the parameters of the model.
Keywords
Cite
@article{arxiv.1709.06748,
title = {Equilibrium fluctuations for the weakly asymmetric discrete Atlas model},
author = {Freddy Hernandez and Marielle Simon},
journal= {arXiv preprint arXiv:1709.06748},
year = {2017}
}