Scaling limits of interacting diffusions in domains
Scaling limits of interacting diffusions in domains作者机构：Department of Mathematics University of Washington Seattle WA 98195 USA
出 版 物：《Frontiers of Mathematics in China》 (中国高等学校学术文摘·数学（英文）)
年 卷 期：2014年第9卷第4期
页 面：717-736页
核心收录：
学科分类：07[理学] 08[工学] 0805[工学-材料科学与工程（可授工学、理学学位）] 080502[工学-材料学] 0701[理学-数学] 0702[理学-物理学]
基 金：国家自然科学基金
主 题：Hydrodynamic limit fluctuation interacting diffusion reflecteddiffusion Dirichlet form non-linear boundary condition coupled partiMdifferential equation martingales stochastic partial differential equation,Guassian process
摘 要：We survey recent effort in establishing the hydrodynamic limits and the fluctuation limits for a class of interacting diffusions in domains. These systems are introduced to model the transport of positive and negative charges in solar cells. They are general microscopic models that can be used to describe macroscopic phenomena with coupled boundary conditions, such as the popula- tion dynamics of two segregated species under competition. Proving these two types of limits represents establishing the functional law of large numbers and the functional central limit theorem, respectively, for the empirical measures of the spatial positions of the particles. We show that the hydrodynamic limit is a pair of deterministic measures whose densities solve a coupled nonlinear heat equations, while the fluctuation limit can be described by a Gaussian Markov process that solves a stochastic partial differential equation.
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