A complete convergence theorem for voter model perturbations

TL;DR

This paper establishes a comprehensive convergence theorem for symmetric voter model perturbations with annihilating duals, including models like the spatial Lotka-Volterra, affine, and geometric voter models, advancing understanding of their long-term behavior.

Contribution

It provides the first complete convergence results for a broad class of voter model perturbations, extending previous partial findings to a unified framework.

Findings

Proves convergence for symmetric voter model perturbations with annihilating duals.

Includes analysis of the spatial Lotka-Volterra model, affine, and geometric voter models.

Establishes conditions under which these models exhibit complete convergence.

Abstract

We prove a complete convergence theorem for a class of symmetric voter model perturbations with annihilating duals. A special case of interest covered by our results is the stochastic spatial Lotka-Volterra model introduced by Neuhauser and Pacala [Ann. Appl. Probab. 9 (1999) 1226-1259]. We also treat two additional models, the "affine" and "geometric" voter models.