The Annals of Probability

Supercritical Contact Processes on $Z$

Richard Durrett and David Griffeath

Full-text: Open access

Abstract

In this paper we introduce a percolation construction which allows us to reduce problems about supercritical contact processes to problems about 1-dependent oriented percolation with density $p$ close to 1. Using this method we obtain a number of results about the growth of supercritical contact processes and the wet region in oriented percolation. As a corollary to our results we find that the critical probability for oriented site percolation is greater than (>) that for bond percolation.

Article information

Source
Ann. Probab., Volume 11, Number 1 (1983), 1-15.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993655

Digital Object Identifier
doi:10.1214/aop/1176993655

Mathematical Reviews number (MathSciNet)
MR682796

Zentralblatt MATH identifier
0508.60080

JSTOR
links.jstor.org

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60F15: Strong theorems

Keywords
Contact processes interacting particle systems oriented percolation large deviations Ceminusgammatee

Citation

Durrett, Richard; Griffeath, David. Supercritical Contact Processes on $Z$. Ann. Probab. 11 (1983), no. 1, 1--15. doi:10.1214/aop/1176993655. https://projecteuclid.org/euclid.aop/1176993655


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