Diffusive clustering in the two dimensional voter model
type: Item
instance of: scholarly article
title: Diffusive clustering in the two dimensional voter model
zbMATH Open document ID: 0658.60131
author: David Griffeath
author: J. Theodore Cox
published in: The Annals of Probability
publication date: 1986-01-01T00:00:00Z
review text: We study the behavior of an interacting particle system known as the voter model in two dimensions. This process provides a simple example of ``critical clustering'' among two colors, say green and black, in the plane. The paper begins with some computer simulations, and a survey of known results concerning the voter model in the three qualitatively distinct cases: three or more dimensions (high), one dimension (low), and two dimensions (critical). Our main theorem, for the planar model, states roughly that at large times t the proportion of green sites on a box of side \(t^{\alpha /2}\) centered at the origin fluctuates with \(\alpha\) according to a time change of the Fisher-Wright diffusion. Some applications of the theorem, and several related results, are described.
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 4076273
zbMATH Keywords: infinite particle system
zbMATH Keywords: voter model
zbMATH Keywords: coalescing random walks
zbMATH Keywords: genetics diffusion
zbMATH Keywords: clustering
zbMATH Keywords: exchangeable random field
zbMATH Keywords: interacting particle system
zbMATH Keywords: computer simulations
zbMATH Keywords: Fisher-Wright diffusion
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176992521
OpenAlex ID: W1993466370
DOI: 10.1214/AOP/1176992521
description: scientific article; zbMATH DE number 4076273