Central Limit Theorem for a Class of Linear Systems

2008/05/03 by Yukio Nagahata, Nagahata, Yukio, Nobuo Yoshida +1
Mathematics · Physics and Astronomy · #60F05 #60J25 (Secondary) #60K35 (Primary) #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #math-ph #math.MP #math.PR #msc:60F05 #msc:60J25 #msc:60K35

paper · pdf · doi:10.48550/arxiv.0805.0342

openalex publication_date 2008/05/03 · arxiv created 2009/06/26 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We consider a class of interacting particle systems with values in [0,\8)^\zd, of which the binary contact path process is an example. For d ≥ 3 and under a certain square integrability condition on the total number of the particles, we prove a central limit theorem for the density of the particles, together with upper bounds for the density of the most populated site and the replica overlap.

Related

• A functional central limit theorem for interacting particle systems on transitive graphs
• Non-equilibrium Fluctuations of the Weakly Asymmetric Normalized Binary Contact Path Process
• Central limit theorems of occupation times of high-dimensional normalized binary contact path processes
• Central limit theorem for a partially observed interacting system of Hawkes processes
• Convergence rates for energies of interacting particles whose distribution spreads out as their number increases