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Equilibrium fluctuations for the weakly asymmetric discrete Atlas model

F Hernández 1 Marielle Simon 2 
2 MEPHYSTO - Quantitative methods for stochastic models in physics
LPP - Laboratoire Paul Painlevé - UMR 8524, Inria Lille - Nord Europe, ULB - Université libre de Bruxelles
Abstract : This contribution aims at presenting and generalizing a recent work of Hernández, Jara and Valentim [10]. We consider the weakly asymmetric version of the so-called discrete Atlas model, which has been introduced in [10]. 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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Submitted on : Thursday, September 21, 2017 - 8:53:33 AM
Last modification on : Wednesday, March 23, 2022 - 3:51:09 PM


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  • HAL Id : hal-01591186, version 1
  • ARXIV : 1709.06748



F Hernández, Marielle Simon. Equilibrium fluctuations for the weakly asymmetric discrete Atlas model. 2017. ⟨hal-01591186⟩



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