Spread of a catalytic branching random walk on a multidimensional lattice

Ekaterina Vl. Bulinskaya

Stochastic Processes and their Applications, 2018, vol. 128, issue 7, 2325-2340

Abstract: For a supercritical catalytic branching random walk on Zd, d∈N, with an arbitrary finite catalysts set we study the spread of particles population as time grows to infinity. It is shown that in the result of the proper normalization of the particles positions in the limit there are a.s. no particles outside the closed convex surface in Rd which we call the propagation front and, under condition of infinite number of visits of the catalysts set, a.s. there exist particles on the propagation front. We also demonstrate that the propagation front is asymptotically densely populated and derive its alternative representation.

Keywords: Branching random walk; Supercritical regime; Spread of population; Propagation front; Many-to-one lemma (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:128:y:2018:i:7:p:2325-2340

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DOI: 10.1016/j.spa.2017.09.007

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