Hostname: page-component-cb9f654ff-hqlzj Total loading time: 0 Render date: 2025-08-21T14:54:30.171Z Has data issue: false hasContentIssue false
  • English
  • Français

The critical contact process on a homogeneous tree

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Gregory J. Morrow ,
Rinaldo B. Schinazi  and
Yu Zhang
Gregory J. Morrow
Affiliation:
University of Colorado at Colorado Springs
Rinaldo B. Schinazi
Affiliation:
University of Colorado at Colorado Springs
Yu Zhang*
Affiliation:
University of Colorado at Colorado Springs
*
∗ Postal address for all authors: Department of Mathematics, University of Colorado at Colorado Springs, 1420 Austin Bluffs Parkway, P.O. Box 7150, Colorado Springs, CO 80933–7150, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove that the expected number of particles of the critical contact process on a homogeneous tree is bounded above. This is the first graph for which the behavior of the expected number of particles of the critical contact process is known. As an easy corollary of our result we get that the critical contact process dies out on any homogeneous tree. This completes the work of Pemantle (1992).

Keywords

INFINITE CONNECTED GRAPHPHASE TRANSITION

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 31 , Issue 1 , March 1994 , pp. 250 - 255
Copyright
Copyright © Applied Probability Trust 1994 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Bezuidenhout, C. and Grimmett, G. (1990) The critical contact process dies out. Ann. Prob. 18, 1462–1482.Google Scholar
Durrett, R. (1988) Lecture Notes on Particle Systems and Percolation. Wadsworth and Brooks Cole, Menlo Park, CA.Google Scholar
Durrett, R. (1991) Probability: Theory and Examples. Wadsworth and Brooks Cole, Menlo Park, CA.Google Scholar
Liggett, T. (1985) Interacting Particle Systems. Springer-Verlag, New York.Google Scholar
Madras, N. and Schinazi, R. (1992) Branching random walks on trees. Stoch. Proc. Appl. 42, 255–267.Google Scholar
Morrow, G. Schinazi, R. and Zhang, Y. (1992) Continuity of the survival probability for the contact process on a tree. Unpublished manuscript.Google Scholar
Pemantle, R. (1992) The contact process on trees. Ann. Prob. 20, 2089–2116.CrossRefGoogle Scholar