Catalytic branching random walk with semi-exponential increments. / Bulinskaya, Ekaterina Vl.
In: Mathematical Population Studies, 2020, p. 1-31.Research output: Contribution to journal › Article › peer-review
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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 -
ID: 27425497