Archive ouverte HAL – A functional central limit theorem for interacting particle systems on transitive graphs

Paul Doukhan ^{1, 2} Gabriel Lang ³ Sana Louhichi ⁴ Bernard Ycart ^{5, 6}

Paul Doukhan, Gabriel Lang, Sana Louhichi, Bernard Ycart. A functional central limit theorem for interacting particle systems on transitive graphs. Markov Processes And Related Fields, Polymat Publishing Company, 2008, 14 (1), pp.79-114. ⟨hal-00268278⟩

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.