Central Limit Theorem for a Tagged Particle in Asymmetric Simple Exclusion

2006/11/16 by Patrícia Gonçalves, Patricia Goncalves, Goncalves, Patricia
Mathematics · #60K35 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #math.PR #msc:60K35

paper · pdf · doi:10.48550/arxiv.math/0611505

28 pages, no figures

openalex publication_date 2006/11/16 · arxiv created 2007/01/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a Functional Central Limit Theorem for the position of a Tagged Particle in the one-dimensional Asymmetric Simple Exclusion Process in the hyperbolic scaling, starting from a Bernoulli product measure conditioned to have a particle at the origin. We also prove that the position of the Tagged Particle at time t depends on the initial configuration, by the number of empty sites in the interval [0,(p-q)αt] divided by α in the hyperbolic and in a longer time scale, namely N^4/3.

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