Quenched nonequilibrium central limit theorem for a tagged particle in the exclusion process with bond disorder

2006/03/28 by M. D. Jara, Cláudio Landim, Jara, M. D. +1 · 3 citations
Mathematics · Physics and Astronomy · #60K35 #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · doi:10.48550/arxiv.math/0603653

openalex publication_date 2006/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a sequence of i.i.d. random variables \ξ_x : x∈ \bb Z\ bounded above and below by strictly positive finite constants, consider the nearest-neighbor one-dimensional simple exclusion process in which a particle at x (resp. x+1) jumps to x+1 (resp. x) at rate ξ_x. We examine a quenched nonequilibrium central limit theorem for the position of a tagged particle in the exclusion process with bond disorder \ξ_x : x∈ \bb Z\. We prove that the position of the tagged particle converges under diffusive scaling to a Gaussian process if the other particles are initially distributed according to a Bernoulli product measure associated to a smooth profile ρ₀:\bb R→ [0,1].

Cited by

• Nonequilibrium fluctuations for the occupation time of the SSEP in d ≥ 2
• Relaxation to equilibrium of conservative dynamics II: non-gradient exclusion processes
• Moderate deviation principles for the current and the tagged particle in the WASEP

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