The Annals of Probability

The Survival of Contact Processes

R. Holley and T. M. Liggett

Full-text: Open access

Abstract

A new proof is given that a contact process on $Z^d$ has a nontrivial stationary measure if the birth rate is sufficiently large. The proof is elementary and avoids the use of percolation processes, which played a key role in earlier proofs. It yields upper bounds for the critical birth rate which are significantly better than those available earlier. In one dimension, these bounds are no more than twice the actual value, and they are no more than four times the actual critical value in any dimension. A lower bound for the particle density of the largest stationary measure is also obtained.

Article information

Source
Ann. Probab., Volume 6, Number 2 (1978), 198-206.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176995567

Digital Object Identifier
doi:10.1214/aop/1176995567

Mathematical Reviews number (MathSciNet)
MR488379

Zentralblatt MATH identifier
0375.60111

JSTOR
links.jstor.org

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
Contact processes infinite particle systems critical phenomena birth and death processes

Citation

Holley, R.; Liggett, T. M. The Survival of Contact Processes. Ann. Probab. 6 (1978), no. 2, 198--206. doi:10.1214/aop/1176995567. https://projecteuclid.org/euclid.aop/1176995567


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