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

Achim Klenke; Leonid Mytnik

doi:10.1214/10-aop621

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arXiv · 0910.4120

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

Achim Klenke·Leonid Mytnik

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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.

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Achim Klenke, Leonid Mytnik. 2009-10-21. Infinite rate mutually catalytic branching in infinitely many colonies: The longtime behavior. https://doi.org/10.1214/10-aop621

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