Hydrodynamic Limits and Propagation of Chaos for Interacting Random Walks in Domains
- Resource Type
- Working Paper
- Authors
- Chen, Zhen-Qing; Fan, Wai-Tong Louis
- Source
- Annals of Applied Probability. Vol. 27, No. 3, 1299-1371 (2017)
- Subject
- Mathematics - Probability
Mathematical Physics
- Language
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.
Comment: 54 pages, 10 figures