The Annals of Probability

The Critical Contact Process Dies Out

Carol Bezuidenhout and Geoffrey Grimmett

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Abstract

By producing a finite-box criterion for survival in a slab, we show that the critical contact process dies out and that, in two and more dimensions, the critical parameter value coincides with the limit of slab thresholds. Using the techniques developed in this paper, one may obtain the complete convergence and shape theorems for contact processes in all dimensions and for all infection rates. Our results apply also to the discrete-time analogue of the contact process, viz., oriented percolation.

Article information

Source
Ann. Probab., Volume 18, Number 4 (1990), 1462-1482.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176990627

Digital Object Identifier
doi:10.1214/aop/1176990627

Mathematical Reviews number (MathSciNet)
MR1071804

Zentralblatt MATH identifier
0718.60109

JSTOR
links.jstor.org

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

Keywords
Contact process oriented percolation

Citation

Bezuidenhout, Carol; Grimmett, Geoffrey. The Critical Contact Process Dies Out. Ann. Probab. 18 (1990), no. 4, 1462--1482. doi:10.1214/aop/1176990627. https://projecteuclid.org/euclid.aop/1176990627


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