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

Wai Tong Fan UW-Madison

Probability mathscidoc:1806.28002

Annals of applied probability, 27, (3), 2017
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.
Hydrodynamic limit, propagation of chaos, interacting particle system, random walk, annihilation, reflecting diffusion, boundary local time, heat kernel, coupled nonlinear partial differential equation, BBGKY hierarchy, Duhamel tree expansion, isoperimetric inequality.
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  • https://projecteuclid.org/euclid.aoap/1500451224
@inproceedings{wai2017hydrodynamic,
  title={HYDRODYNAMIC LIMITS AND PROPAGATION OF CHAOS FOR INTERACTING RANDOM WALKS IN DOMAINS},
  author={Wai Tong Fan},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180619025122448622107},
  booktitle={Annals of applied probability},
  volume={27},
  number={3},
  year={2017},
}
Wai Tong Fan. HYDRODYNAMIC LIMITS AND PROPAGATION OF CHAOS FOR INTERACTING RANDOM WALKS IN DOMAINS. 2017. Vol. 27. In Annals of applied probability. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180619025122448622107.
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