Hostname: page-component-6bb9c88b65-lm65w Total loading time: 0.006 Render date: 2025-07-26T08:50:05.904Z Has data issue: false hasContentIssue false
  • English
  • Français

A Metastable Result for the Finite Multidimensional Contact Process

Published online by Cambridge University Press:  20 November 2018

T. S. Mountford
T. S. Mountford*
Affiliation:
T. S. Mountford Department of Mathematics University of California Los Angeles, California 90024 U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We prove that for a contact process restricted to the cube [1,n]d and initially fully occupied, the time to die out, when it is suitably normalized, converges to an exponential random variable as n tends to infinity.

Keywords

60K35contact processmetastability

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 36 , Issue 2 , 01 June 1993 , pp. 216 - 226
Copyright
Copyright © Canadian Mathematical Society 1993

References

Bezuidenhout, C. and Grimmet, G. (1990), The critical contact process dies out, Annals of Probability 18, 1462–1482.Google Scholar
Cassandro, M., Galves, A., Olivieri, E. and Vares, M. (1984), Metastable behaviour of stochastic dynamics: a pathwise approach, Journal Stat. Phys. 35, 603-634.Google Scholar
Durrett, R. (1984), Oriented percolation in two dimensions, Annals of Probability 12, 999-1040. (1988), Lecture Notes on Particle Systems and Percolation, Wadsworth and Brooks/Cole, Pacific Grove, California.Google Scholar
Durrett, R. and Schonmann, R. (1988), The contact provess on a finite set II, Annals of Probability 16,1570– 1583.Google Scholar
Liggett, T. (1985), Interacting Particle Systems, Springer, New York.Google Scholar
Schonmann, R. (1985), Metastability for the contact process, Journal Stat. Phys. 41,445–464.Google Scholar