Open Access
Translator Disclaimer
April, 1978 The Survival of Contact Processes
R. Holley, T. M. Liggett
Ann. Probab. 6(2): 198-206 (April, 1978). DOI: 10.1214/aop/1176995567


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.


Download Citation

R. Holley. T. M. Liggett. "The Survival of Contact Processes." Ann. Probab. 6 (2) 198 - 206, April, 1978.


Published: April, 1978
First available in Project Euclid: 19 April 2007

zbMATH: 0375.60111
MathSciNet: MR488379
Digital Object Identifier: 10.1214/aop/1176995567

Primary: 60K35

Keywords: birth and death processes , contact processes , Critical phenomena , infinite particle systems

Rights: Copyright © 1978 Institute of Mathematical Statistics


Vol.6 • No. 2 • April, 1978
Back to Top