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arXiv · 1612.09025

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

Kaizheng Wang
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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 $L^2$ 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.

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Kaizheng Wang. 2016-12-29. Stochastic Representations for the Wave Equation on Graphs and their Scaling Limits. https://doi.org/10.1016/j.jmaa.2016.12.003

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