The Annals of Applied Probability

The contact process in a dynamic random environment

Daniel Remenik

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Abstract

We study a contact process running in a random environment in ℤd where sites flip, independently of each other, between blocking and nonblocking states, and the contact process is restricted to live in the space given by nonblocked sites. We give a partial description of the phase diagram of the process, showing in particular that, depending on the flip rates of the environment, survival of the contact process may or may not be possible for large values of the birth rate. We prove block conditions for the process that parallel the ones for the ordinary contact process and use these to conclude that the critical process dies out and that the complete convergence theorem holds in the supercritical case.

Article information

Source
Ann. Appl. Probab., Volume 18, Number 6 (2008), 2392-2420.

Dates
First available in Project Euclid: 26 November 2008

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1227708923

Digital Object Identifier
doi:10.1214/08-AAP528

Mathematical Reviews number (MathSciNet)
MR2474541

Zentralblatt MATH identifier
1181.60153

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

Keywords
Contact process random environment complete convergence block construction interacting particle system

Citation

Remenik, Daniel. The contact process in a dynamic random environment. Ann. Appl. Probab. 18 (2008), no. 6, 2392--2420. doi:10.1214/08-AAP528. https://projecteuclid.org/euclid.aoap/1227708923


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