Stochastic representations for the wave equation on graphs and their scaling limits

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:449

Article

Wang, Kaizheng¹ 

[1] Princeton Univ, Dept Operat Res & Financial Engn, Sherrerd Hall,Charlton St, Princeton, NJ 08544 USA

关键词: Wave equation;    Interacting particle system;    Graph;    Hydrodynamic limits;    Phase transition;   

DOI  :  10.1016/j.jmaa.2016.12.003

来源: Elsevier

【 摘 要 】

This paper is devoted to an interacting particle system that provides probabilistic interpretation of the wave equation on graphs. A Feynrnan-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. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free