Stochastic spatial models

Journal Article (Journal Article)

In the models we will consider, space is represented by a grid of sites that can be in one of a finite number of states and that change at rates that depend on the states of a finite number of sites. Our main aim here is to explain an idea of Durrett and Levin (1994): the behavior of these models can be predicted from the properties of the mean field ODE, i.e., the equations for the densities of the various types that result from pretending that all sites are always independent. We will illustrate this picture through a discussion of eight families of examples from statistical mechanics, genetics, population biology, epidemiology, and ecology. Some of our findings are only conjectures based on simulation, but in a number of cases we are able to prove results for systems with `fast stirring' by exploiting connections between the spatial model and an associated reaction diffusion equation.

Full Text

Duke Authors

Cited Authors

  • Durrett, R

Published Date

  • January 1, 1999

Published In

Volume / Issue

  • 41 / 4

Start / End Page

  • 677 - 718

International Standard Serial Number (ISSN)

  • 0036-1445

Digital Object Identifier (DOI)

  • 10.1137/S0036144599354707

Citation Source

  • Scopus