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arXiv · 1709.06748

Equilibrium fluctuations for the weakly asymmetric discrete Atlas model

Freddy Hernandez·Marielle Simon
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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.

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Freddy Hernandez, Marielle Simon. 2017-09-20. Equilibrium fluctuations for the weakly asymmetric discrete Atlas model. https://arxiv.org/abs/1709.06748

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