Hydrodynamic limits and propagation of chaos for interacting random walks in domains

Zhen Qing Chen, Wai Tong Fan

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)1299-1371
Number of pages73
JournalAnnals of Applied Probability
Volume27
Issue number3
DOIs
Publication statusPublished - Jun 2017
Externally publishedYes

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

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