The Annals of Probability
- Ann. Probab.
- Volume 40, Number 1 (2012), 103-129.
Infinite rate mutually catalytic branching in infinitely many colonies: The longtime behavior
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.
Ann. Probab., Volume 40, Number 1 (2012), 103-129.
First available in Project Euclid: 3 January 2012
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60J65: Brownian motion [See also 58J65] 60G17: Sample path properties 60J55: Local time and additive functionals 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Klenke, Achim; Mytnik, Leonid. Infinite rate mutually catalytic branching in infinitely many colonies: The longtime behavior. Ann. Probab. 40 (2012), no. 1, 103--129. doi:10.1214/10-AOP621. https://projecteuclid.org/euclid.aop/1325604998