Open Access
June 2017 Hydrodynamic limits and propagation of chaos for interacting random walks in domains
Zhen-Qing Chen, Wai-Tong (Louis) Fan
Ann. Appl. Probab. 27(3): 1299-1371 (June 2017). DOI: 10.1214/16-AAP1208

Abstract

A new non-conservative stochastic reaction–diffusion system in which two families of random walks in two adjacent domains interact near the interface is introduced and studied in this paper. Such a system can be used to model the transport of positive and negative charges in a solar cell or the population dynamics of two segregated species under competition. We show that in the macroscopic limit, the particle densities converge to the solution of a coupled nonlinear heat equations. For this, we first prove that propagation of chaos holds by establishing the uniqueness of a new BBGKY hierarchy. A local central limit theorem for reflected diffusions in bounded Lipschitz domains is also established as a crucial tool.

Citation

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Zhen-Qing Chen. Wai-Tong (Louis) Fan. "Hydrodynamic limits and propagation of chaos for interacting random walks in domains." Ann. Appl. Probab. 27 (3) 1299 - 1371, June 2017. https://doi.org/10.1214/16-AAP1208

Information

Received: 1 September 2014; Revised: 1 February 2016; Published: June 2017
First available in Project Euclid: 19 July 2017

zbMATH: 1372.60133
MathSciNet: MR3678472
Digital Object Identifier: 10.1214/16-AAP1208

Subjects:
Primary: 60F17 , 60K35
Secondary: 92D15

Keywords: annihilation , BBGKY hierarchy , boundary local time , coupled nonlinear partial differential equation , Duhamel tree expansion , heat kernel , Hydrodynamic limit , Interacting particle system , Isoperimetric inequality , propagation of chaos , Random walk , reflecting diffusion

Rights: Copyright © 2017 Institute of Mathematical Statistics

Vol.27 • No. 3 • June 2017
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