Infinite Rate Mutually Catalytic Branching in Infinitely Many Colonies: The Longtime Behaviour

Details Infinite Rate Mutually Catalytic Branching in Infinitely Many Colonies: The Longtime Behaviour Infinite Rate Mutually Catalytic Branching in Infinitely Many Colonies: The Longtime Behaviour

2009-10-21

arxiv.org/abs/0910.4120v1

Mathematics

Probability

Scientific paper

Consider the infinite rate mutually catalytic branching process (IMUB)
constructed in [Klenke and Mytnik 2008] and [Klenke and Oeler 2009]. We show
that for finite initial condition 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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