Infinite rate mutually catalytic branching in infinitely many colonies: The longtime behavior

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.

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)

References in corpus (2)

• A Trotter-type approach to infinite rate mutually catalytic branching
• Infinite rate mutually catalytic branching

Cited by in corpus (5)

• On the moments and the interface of the symbiotic branching model
• A Trotter-type approach to infinite rate mutually catalytic branching
• Infinite rate mutually catalytic branching
• The scaling limit of the interface of the continuous-space symbiotic branching model
• The symbiotic branching model: duality and interfaces