Infinite rate mutually catalytic branching in infinitely many colonies: The longtime behavior
Probability
2012-09-26 v2
Abstract
Consider the infinite rate mutually catalytic branching process (IMUB) constructed in [Infinite rate mutually catalytic branching in infinitely many colonies. Construction, characterization and convergence (2008) Preprint] and [Ann. Probab. 38 (2010) 479-497]. For finite initial conditions, we show that only one type survives in the long run if the interaction kernel is recurrent. On the other hand, under a slightly stronger condition than transience, we show that both types can coexist.
Keywords
Cite
@article{arxiv.0910.4120,
title = {Infinite rate mutually catalytic branching in infinitely many colonies: The longtime behavior},
author = {Achim Klenke and Leonid Mytnik},
journal= {arXiv preprint arXiv:0910.4120},
year = {2012}
}
Comments
Published in at http://dx.doi.org/10.1214/10-AOP621 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)