The Local Time Distribution of a Particle Diffusing on a Graph

Alain Comtet (1, 2) , Jean Desbois (1) , Satya N. Majumdar (3)

1 LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
2 IHP - Institut Henri Poincaré
3 GPT-LPQ - Groupe de Physique Théorique (LPQ)

We study the local time distribution of a Brownian particle diffusing along the links on a graph. In particular, we derive an analytic expression of its Laplace transform in terms of the Green's function on the graph. We show that the asymptotic behavior of this distribution has non-Gaussian tails characterized by a nontrivial large deviation function.

Mots clés: Statistical Mechanics

Domaines: Mécanique statistique [cond-mat.stat-mech]

Alain Comtet, Jean Desbois, Satya N. Majumdar. The Local Time Distribution of a Particle Diffusing on a Graph. Journal of Physics A: Mathematical and Theoretical, 2002, 35, pp.L687-L694. ⟨hal-00002332⟩