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 Electronic Journal of Probability > Vol. 4 (1999) > Paper 12 open journal systems 


The Longtime Behavior of Branching Random Walk in a Catalytic Medium

Andreas Greven, Universitat Erlangen-Nurnberg
Achim Klenke, Universität Erlangen - Nürnberg
Anton Wakolbinger, Johann Wolfgang Goethe-Universität


Abstract
Consider a countable collection of particles located on a countable group, performing a critical branching random walk where the branching rate of a particle is given by a random medium fluctuating both in space and time. Here we study the case where the time-space random medium (called catalyst) is also a critical branching random walk evolving autonomously while the local branching rate of the reactant process is proportional to the number of catalytic particles present at a site. The catalyst process and the reactant process typically have different underlying motions.


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Pages: 1-80

Published on: April 6, 1999
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Electronic Journal of Probability. ISSN: 1083-6489