Electronic Journal of Probability

The Longtime Behavior of Branching Random Walk in a Catalytic Medium

Andreas Greven, Achim Klenke, and Anton Wakolbinger

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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.

Article information

Electron. J. Probab., Volume 4 (1999), paper no. 12, 80 pp.

Accepted: 6 April 1999
First available in Project Euclid: 4 March 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Branching random walk in random medium reactant-catalyst systems interacting particle Systems random media

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Greven, Andreas; Klenke, Achim; Wakolbinger, Anton. The Longtime Behavior of Branching Random Walk in a Catalytic Medium. Electron. J. Probab. 4 (1999), paper no. 12, 80 pp. doi:10.1214/EJP.v4-49. https://projecteuclid.org/euclid.ejp/1457125521

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