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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