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October, 1981 A Note on the Survival of the Long-Range Contact Process
Maury Bramson, Lawrence Gray
Ann. Probab. 9(5): 885-890 (October, 1981). DOI: 10.1214/aop/1176994316


The purpose of this note is to demonstrate survival for the long-range contact process. This process was introduced by Spitzer [7]; it possesses the same basic evolutionary rule as does the contact process on the integers, except that particles may appear at large distances from already extant particles instead of just as immediate neighbors. We consider here two variants of this model, and show that in both cases the system will survive if (i) it commences from a reasonably dense initial state and (ii) the birth rate for particles is moderately greater than the corresponding death rate. The methodology consists primarily of an energy argument, which provides a lower bound for the particle density of the system.


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Maury Bramson. Lawrence Gray. "A Note on the Survival of the Long-Range Contact Process." Ann. Probab. 9 (5) 885 - 890, October, 1981.


Published: October, 1981
First available in Project Euclid: 19 April 2007

zbMATH: 0467.60090
MathSciNet: MR628881
Digital Object Identifier: 10.1214/aop/1176994316

Primary: 60K35

Keywords: contact process , Interacting particle system , long-range contact process

Rights: Copyright © 1981 Institute of Mathematical Statistics


Vol.9 • No. 5 • October, 1981
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