Systems of interacting diffusions with partial annihilation through membranes

Zhen-Qing Chen, Wai-Tong (Louis) Fan
2017 Annals of Probability  
We introduce an interacting particle system in which two families of reflected diffusions interact in a singular manner near a deterministic interface $I$. 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
more » ... ish 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.
doi:10.1214/15-aop1047 fatcat:bei7nlyfrjecfot3wkevcaub4q