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Matematicheskie Zametki, 2012, Volume 92, Issue 1, Pages 123–140
DOI: https://doi.org/10.4213/mzm9485 (Mi mzm9485) 		 
This article is cited in 30 scientific papers (total in 30 papers)

Spectral Properties of Evolutionary Operators in Branching Random Walk Models

E. B. Yarovaya

M. V. Lomonosov Moscow State University
Full-text PDF (637 kB) Citations (30)
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DOI: https://doi.org/10.4213/mzm9485
Abstract: We introduce a model of continuous-time branching random walk on a finite-dimensional integer lattice with finitely many branching sources of three types and study the spectral properties of the operator describing the evolution of the average numbers of particles both at an arbitrary source and on the entire lattice. For the leading positive eigenvalue of the operator, we obtain existence conditions determining exponential growth in the number of particles in this model.
Keywords: branching random walk, equations in Banach spaces, pseudodifference operator, symmetrizable operator, positive eigenvalue.
Received: 05.04.2011
Revised: 21.04.2011
English version:
Mathematical Notes, 2012, Volume 92, Issue 1, Pages 115–131
DOI: https://doi.org/10.1134/S0001434612070139
Bibliographic databases:
Document Type: Article
UDC: 517.984.5+519.21
Language: Russian
Citation: E. B. Yarovaya, “Spectral Properties of Evolutionary Operators in Branching Random Walk Models”, Mat. Zametki, 92:1 (2012), 123–140; Math. Notes, 92:1 (2012), 115–131
Citation in format AMSBIB
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    • This publication is cited in the following 30 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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