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

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References

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