Spread of a catalytic branching random walk on a multidimensional lattice |
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Authors: | Ekaterina Vl. Bulinskaya |
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Affiliation: | Lomonosov Moscow State University, Faculty of Mathematics and Mechanics, Leninskie gory 1, Moscow 119991, Russia |
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Abstract: | For a supercritical catalytic branching random walk on , , 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 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. |
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Keywords: | 60J80 60F15 Branching random walk Supercritical regime Spread of population Propagation front Many-to-one lemma |
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