Individuals at the origin in the critical catalytic branching random walk
Authors: Valentin Topchii 1; Vladimir Vatutin 2
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Valentin Topchii;Vladimir Vatutin
1 Omsk branch of Sobolev Institute of Mathematics
2 Steklov Mathematical Institute [Moscow]
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.
Carmona, Philippe; Hu, Yueyun, 2014, The Spread Of A Catalytic Branching Random Walk, Annales De l'Institut Henri PoincarĂŠ, ProbabilitĂŠs Et Statistiques, 50, 2, 10.1214/12-aihp529.