The Local Time Distribution of a Particle Diffusing on a Graph

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.

8 pages, two figures (included)

References in corpus (3)

• The Local and the Occupation Time of a Particle Diffusing in a Random Medium
• Large-Deviation Functions for Nonlinear Functionals of a Gaussian Stationary Markov Process
• Scattering theory on graphs

Cited by in corpus (16)

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• Brownian Motions on Metric Graphs
• First-passage Brownian functionals with stochastic resetting
• No quantum ergodicity for star graphs
• Local time for run and tumble particle
• First-passage functionals for Ornstein Uhlenbeck process with stochastic resetting
• Encounter-based approach to diffusion with resetting
• Exit and Occupation times for Brownian Motion on Graphs with General Drift and Diffusion Constant
• Large deviations in statistics of the local time and occupation time for a run and tumble particle
• Macroscopic fluctuation theory of local time in lattice gases
• Local time of an Ornstein-Uhlenbeck particle
• $\zeta$-regularised spectral determinants on metric graphs
• Dimensionality-induced dynamical phase transition in the large deviation of local time density for Brownian motion