The Local Time Distribution of a Particle Diffusing on a Graph

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

Journal of Physics A 35 (2002) L687-L694

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.

  • 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud
  • 2. IHP,
    Institut Henri Poincaré
  • 3. Laboratoire de Physique Quantique (LPQ),
    CNRS : UMR5626 – Université Paul Sabatier - Toulouse III