A Functional Central Limit Theorem for Interacting Particle Systems on Transitive Graphs

P. Doukhan, G. Lang, S. Louhichi, B. Ycart

2008, v.14, Issue 1, 79-114

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.

Keywords: interacting particle system,functional central limit theorem,hitting time