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