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Individuals at the origin in the critical catalytic branching random walk

Abstract : A continuous time branching random walk on the lattice $\mathbb{Z}$ is considered in which individuals may produce children at the origin only. Assuming that the underlying random walk is symmetric and the offspring reproduction law is critical we prove a conditional limit theorem for the number of individuals at the origin.
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Valentin Topchii, Vladimir Vatutin. Individuals at the origin in the critical catalytic branching random walk. Discrete Random Walks, DRW'03, 2003, Paris, France. pp.325-332. ⟨hal-01183926⟩

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