Structure of the Particle Population for a Branching Random Walk with a Critical Reproduction Law

Daria Balashova (), Stanislav Molchanov () and Elena Yarovaya ()
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Daria Balashova: Lomonosov Moscow State University
Stanislav Molchanov: University of North Carolina at Charlotte
Elena Yarovaya: Lomonosov Moscow State University

Methodology and Computing in Applied Probability, 2021, vol. 23, issue 1, 85-102

Abstract: Abstract We consider a continuous-time symmetric branching random walk on the d-dimensional lattice, d ≥ 1, and assume that at the initial moment there is one particle at every lattice point. Moreover, we assume that the underlying random walk has a finite variance of jumps and the reproduction law is described by a continuous-time Markov branching process (a continuous-time analog of a Bienamye-Galton-Watson process) at every lattice point. We study the structure of the particle subpopulation generated by the initial particle situated at a lattice point x. We replay why vanishing of the majority of subpopulations does not affect the convergence to the steady state and leads to clusterization for lattice dimensions d = 1 and d = 2.

Keywords: Branching random walk; Critical branching process; Limit theorems; Population dynamics; 60J80; 60G50; 60F99 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11009-020-09773-2

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