Open Access
October, 1990 The Critical Contact Process Dies Out
Carol Bezuidenhout, Geoffrey Grimmett
Ann. Probab. 18(4): 1462-1482 (October, 1990). DOI: 10.1214/aop/1176990627


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.


Download Citation

Carol Bezuidenhout. Geoffrey Grimmett. "The Critical Contact Process Dies Out." Ann. Probab. 18 (4) 1462 - 1482, October, 1990.


Published: October, 1990
First available in Project Euclid: 19 April 2007

zbMATH: 0718.60109
MathSciNet: MR1071804
Digital Object Identifier: 10.1214/aop/1176990627

Primary: 60K35

Keywords: contact process , Oriented percolation

Rights: Copyright © 1990 Institute of Mathematical Statistics

Vol.18 • No. 4 • October, 1990
Back to Top