The Spread of a Catalytic Branching Random Walk

Mathematics – Probability

Scientific paper

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34 pages, submitted

Scientific paper

We consider a random walk on $\Z$ that branches at the origin only. In the
supercritical regime we establish a law of large number for the maximal
position $M_n$. Then we prove convergence in distribution for the sequence $M_n
-\alpha n$ where $\alpha$ is a deterministic constant.

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