The Local Time Distribution of a Particle Diffusing on a Graph

TL;DR

This paper derives an analytic expression for the local time distribution of a Brownian particle on a graph, revealing non-Gaussian tails and large deviation behavior in its asymptotics.

Contribution

It provides a new analytic formula for the local time distribution on graphs using Green's functions, highlighting non-Gaussian tail behavior.

Findings

Laplace transform expressed via Green's function

Asymptotic distribution exhibits non-Gaussian tails

Large deviation function characterizes tail behavior

Abstract

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.