Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-26T23:09:49.958Z Has data issue: false hasContentIssue false
  • English
  • Français

Stochastic order for invariant measures of the contact process

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

E. D. Andjel
E. D. Andjel*
Affiliation:
CMI, Marseille
*
∗Postal address: CMI, 39 rue Joliot Curie, 13453 Marseille cedex 13, France. Email address: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We show that the second lowest invariant measure of the contact process, introduced by Salzano and Schonmann (1997), is stochastically lower that any invariant measure which puts no mass on the empty configuration.

Keywords

Contact processstochastic ordersecond lowest invariant measure

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Type
Short Communications
Information
Journal of Applied Probability , Volume 40 , Issue 4 , September 2003 , pp. 1155 - 1157
Copyright
Copyright © Applied Probability Trust 2003 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Griffeath, D. (1979). Additive and Cancellative Interacting Particle Systems (Lecture Notes Math. 724). Springer, Berlin.Google Scholar
Griffeath, D. (1981). The basic contact process. Stoch. Process. Appl. 11, 151–186.Google Scholar
Harris, T. (1974). Contact interactions on a lattice. Ann. Prob. 2, 969–988.Google Scholar
Liggett, T. M. (1985). Interacting Particle Systems. Springer, New York.CrossRefGoogle Scholar
Liggett, T. M. (1999). Stochastic Interacting Systems: Contact, Voter and Exclusion Processes. Springer, Berlin.CrossRefGoogle Scholar
Salzano, M., and Schonmann, R. H. (1997). The second lowest extremal invariant measure of the contact process. Ann. Prob. 25, 1846–1871.CrossRefGoogle Scholar