TY - JOUR

T1 - Catalytic branching random walk with semi-exponential increments

AU - Bulinskaya, Ekaterina Vl

N1 - Funding Information: This work was supported by the Russian Science Foundation [17-11-01173] and was conducted at Novosibirsk State University. The author is Associate Professor at Lomonosov Moscow State University. The author is very grateful to two reviewers for their helpful comments. Publisher Copyright: © 2020, © 2020 Taylor & Francis. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020

Y1 - 2020

N2 - In a catalytic branching random walk on a multidimensional lattice, with arbitrary finite total number of catalysts, in supercritical regime, when the vector coordinates of the random walk jump are assumed independent (or close to independent) to one another and have semi-exponential distributions, a limit theorem provides the almost sure normalized locations of the particles at the boundary between populated and empty areas. Contrary to the case of random walk increments with light distribution tails, the normalizing factor grows faster than linearly over time. The limit shape of the front in the case of semi-exponential tails is no longer convex, as it is in the case of light tails.

AB - In a catalytic branching random walk on a multidimensional lattice, with arbitrary finite total number of catalysts, in supercritical regime, when the vector coordinates of the random walk jump are assumed independent (or close to independent) to one another and have semi-exponential distributions, a limit theorem provides the almost sure normalized locations of the particles at the boundary between populated and empty areas. Contrary to the case of random walk increments with light distribution tails, the normalizing factor grows faster than linearly over time. The limit shape of the front in the case of semi-exponential tails is no longer convex, as it is in the case of light tails.

KW - Catalytic branching random walk

KW - heavy tails

KW - propagation front

KW - propagation of population

KW - semi-exponential distribution tails

KW - supercritical regime

KW - NUMBER

KW - SPREAD

UR - http://www.scopus.com/inward/record.url?scp=85087814706&partnerID=8YFLogxK

U2 - 10.1080/08898480.2020.1767424

DO - 10.1080/08898480.2020.1767424

M3 - Article

AN - SCOPUS:85087814706

SP - 1

EP - 31

JO - Mathematical Population Studies

JF - Mathematical Population Studies

SN - 0889-8480

ER -