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