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

Paul Doukhan·Gabriel Lang·Sana Louhichi·Bernard Ycart
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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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Paul Doukhan, Gabriel Lang, Sana Louhichi, Bernard Ycart. 2007-04-12. A functional central limit theorem for interacting particle systems on transitive graphs. https://arxiv.org/abs/math-ph/0509041

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