The Annals of Probability

The Survival of Contact Processes

R. Holley and T. M. Liggett

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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

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

First available in Project Euclid: 19 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


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

Contact processes infinite particle systems critical phenomena birth and death processes


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

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