The longtime behavior of branching random walk in a catalytic medium

  • We consider catalytic branching random walk (the reactant) where the state space is a countable Abelean group. The branching is critical binary and the local branching rate is given by a catalytic medium. Here the medium is itself an autonomous (ordinary) branching random walk (the catalyst) - maybe with a different motion law. For persistent catalyst (transient motion) the reactant shows the usual dichotomy of persistence versus extinction depending on transience or recurrence of its motion. If the catalyst goes to local extinction it turns out that the longtime behaviour of the reactant ranges (depending on its motion) from local extinction to free random walk with either deterministic or random global intensity of particles.

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Author:Andreas Greven, Achim Klenke, Anton WakolbingerGND
Parent Title (English):Electronic journal of probability
Publisher:EMIS ELibEMS
Place of publication:[Madralin]
Document Type:Article
Year of Completion:2014
Year of first Publication:1999
Publishing Institution:Universit├Ątsbibliothek Johann Christian Senckenberg
Release Date:2014/01/29
Tag:branching random walk in random medium; interacting particle Systems; random media; reactant-catalyst systems
Page Number:80
This work is licensed under a Creative Commons Attribution 3.0 License .
Institutes:Informatik und Mathematik / Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC-Classification:60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Kxx Special processes / 60K35 Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Licence (German):License LogoCreative Commons - Namensnennung 3.0