Systems of interacting diffusions with partial annihilation through membranes
Abstract
We introduce an interacting particle system in which two families of reflected diffusions interact in a singular manner near a deterministic interface . This 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. A related interacting random walk model with discrete state spaces has recently been introduced and studied in Chen and Fan (2014). In this paper, we establish the functional law of large numbers for this new system, thereby extending the hydrodynamic limit in Chen and Fan (2014) to reflected diffusions in domains with mixed-type boundary conditions, which include absorption (harvest of electric charges). We employ a new and direct approach that avoids going through the delicate BBGKY hierarchy.
Cite
@article{arxiv.1403.5903,
title = {Systems of interacting diffusions with partial annihilation through membranes},
author = {Zhen-Qing Chen and Wai-Tong Fan},
journal= {arXiv preprint arXiv:1403.5903},
year = {2021}
}
Comments
Published at http://dx.doi.org/10.1214/15-AOP1047 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)