Atypical behaviors of a tagged particle in asymmetric simple exclusion

2023/11/13 by Sunder Sethuraman, Sethuraman, Sunder, S. R. S. Varadhan +1 · 1 citation
Mathematics · Physics and Astronomy · #60K35 #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Quantum Mechanics and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2311.07800

openalex publication_date 2023/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider the asymmetric nearest-neighbor exclusion process (ASEP) on \mathbb Z with single particle drift γ>0, starting from a Bernoulli product invariant measure ν_ρ with density ρ. It is known that the position X_N of a tagged particle, say initially at the origin, at time N satisfies an a.s. law of large numbers (1)/(N)X_N → γ(1-ρ) as N\uparrow∞. In this context, we study the `typical' behavior of the tagged particle and `bulk' density evolution subject to `atypical' events \X_N≥ AN\ or \X_N≤ AN\ for A≠ γ(1-ρ). We detail different structures, depending on whether A<0, 0≤ A< γ(1-ρ), γ(1-ρ)

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• Moderate deviation principles for the current and the tagged particle in the WASEP

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