Open Access
Translator Disclaimer
January 2017 Systems of interacting diffusions with partial annihilation through membranes
Zhen-Qing Chen, Wai-Tong (Louis) Fan
Ann. Probab. 45(1): 100-146 (January 2017). DOI: 10.1214/15-AOP1047


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 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.


Download Citation

Zhen-Qing Chen. Wai-Tong (Louis) Fan. "Systems of interacting diffusions with partial annihilation through membranes." Ann. Probab. 45 (1) 100 - 146, January 2017.


Received: 1 June 2014; Revised: 1 July 2015; Published: January 2017
First available in Project Euclid: 26 January 2017

zbMATH: 1361.60088
MathSciNet: MR3601647
Digital Object Identifier: 10.1214/15-AOP1047

Primary: 60F17 , 60K35
Secondary: 92D15

Keywords: annihilation , coupled partial differential equation , Dirichlet form , Hydrodynamic limit , Interacting diffusion , Martingales , nonlinear boundary condition , Reflected diffusion

Rights: Copyright © 2017 Institute of Mathematical Statistics


Vol.45 • No. 1 • January 2017
Back to Top