The Annals of Probability
- Ann. Probab.
- Volume 18, Number 4 (1990), 1462-1482.
The Critical Contact Process Dies Out
Carol Bezuidenhout and Geoffrey Grimmett
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
