SYSTEMS OF INTERACTING DIFFUSIONS WITH PARTIAL ANNIHILATION THROUGH MEMBRANES'

• 成果类型: Article
• 署名作者: Chen, Zhen-Qing; Fan, Wai-Tong (Louis)
• 署名单位: University of Washington; University of Washington Seattle; University of North Carolina; University of North Carolina Chapel Hill
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/15-AOP1047
• 发表日期: 2017
• 页码: 100-146
• 关键词: chemical-reactions; potential-theory; limit; fluctuations; EQUATIONS; MODEL

摘要

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.