Diffusive to super-diffusive behavior in boundary driven exclusion

2020/04/08 by Patrícia Gonçalves, Gonçalves, Patrícia, Stefano Scotta +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2004.03978

openalex publication_date 2020/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The purpose of this article is to study the hydrodynamic limit of the symmetric exclusion process with long jumps and in contact with infinitely extended reservoirs for a particular critical regime. The jumps are given in terms of a transition probability that can have finite or infinite variance and the hydrodynamic equation is a diffusive equation, in the former case, or a fractional equation, in the latter case. In this work we treat the critical case, that is, when the variance is infinite and grows logarithmically with the size of the system. This is the case in which there is a transition from diffusive to super-diffusive behavior.

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