Abstract
We consider branching Markov chains on a countable set. We give a necessary and sufficient condition in terms of the transition kernel of the underlying Markov chain to have two phase transitions. We compute the critical values. We apply this result to prove that asymmetric branching random walks onZ have two phase transitions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
C. Bezuidenhout and G. Grimmett, The critical contact process dies out,Ann. Prob. 18:1462–1482 (1990).
R. Durrett,Lecture Notes on Particle Systems and Percolation (Wadsworth and Brooks/Cole, Pacific Grove, California, 1988).
T. Liggett,Interacting Particle Systems (Springer-Verlag, Berlin, 1985).
N. Madras and R. Schinazi, Branching random walks on trees,Stochastic Processes Appl. 42:255–267 (1992).
R. Pemantle, The contact process on trees,Ann. Prob. 20:2089–2116 (1992).
R. Schonmann, The asymmetric contact process,J. Stat. Phys. 44:505–534 (1986).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Schinazi, R. On multiple phase transitions for branching Markov chains. J Stat Phys 71, 507–511 (1993). https://doi.org/10.1007/BF01058434
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01058434