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.

• 1. SAMOS – Statistique Appliquée et MOdélisation Stochastique
• 2. CES – Centre d’économie de la Sorbonne
• 3. MIA-Paris – Mathématiques et Informatique Appliquées
• 4. LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
• 5. SMS – Statistique et Modélisation Stochatisque
• 6. MAP5 – UMR 8145 – Mathématiques Appliquées Paris 5