paper

Stochastic Representations for the Wave Equation on Graphs and their Scaling Limits

arXiv:1612.09025 · doi:10.1016/j.jmaa.2016.12.003

Abstract

This paper is devoted to an interacting particle system that provides probabilistic interpretation of the wave equation on graphs. A Feynman-Kac-type formula is established, connecting the expectation of the process with the wave equation on graphs. Non-asymptotic estimates are presented. It is then shown that the high-density hydrodynamic limit of the system is given by the wave equation in Euclidean space. The sharpness of scaling limit result is demonstrated by a phase transition phenomenon.

28 pages in J. Math. Anal. Appl. (2017)

Stochastic Representations for the Wave Equation on Graphs and their Scaling Limits · wovepaper