The Local Time Distribution of a Particle Diffusing on a Graph
  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. 
Alain Comtet, Jean Desbois and Satya N. Majumdar