A functional central limit theorem for interacting particle systems on transitive graphs

2005/09/19 by Paul Doukhan, Gabriel Lang, Doukhan, Paul +5 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Diffusion and Search Dynamics #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and statistical mechanics #math-ph #math.MP #math.PR

paper · pdf · doi:10.48550/arxiv.math-ph/0509041

35 pages

openalex publication_date 2005/09/19 · arxiv created 2007/04/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A finite range interacting particle system on a transitive graph is considered. Assuming that the dynamics and the initial measure are invariant, the normalized empirical distribution process converges in distribution to a centered diffusion process. As an application, a central limit theorem for certain hitting times, interpreted as failure times of a coherent system in reliability, is derived.

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• Existence and spatial limit theorems for lattice and continuum particle systems

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