Limits of One-dimensional Interacting Particle Systems with Two-scale Interaction

Abstract

This paper characterizes the limits of a large system of interacting particles distributed on the real line. The interaction occurring among neighbors involves two kinds of independent actions with different rates. This system is a generalization of the voter process, of which each particle is of type A or a. Under suitable scaling, the local proportion functions of A particles converge to continuous functions which solve a class of stochastic partial differential equations driven by Fisher-Wright white noise. To obtain the convergence, the tightness of these functions is derived from the moment estimate method.

Keywords

Interacting particle systems / Stochastic partial differential equations / Two-scale interaction / Tightness

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