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Teoriya Veroyatnostei i ee Primeneniya, 2017, Volume 62, Issue 3, Pages 518–541
DOI: https://doi.org/10.4213/tvp5111 (Mi tvp5111) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Spectral asymptotics of supercritical branching random process

E. B. Yarovaya

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Full-text PDF (676 kB) Citations (11)
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DOI: https://doi.org/10.4213/tvp5111
Abstract: The paper is concerned with supercritical continuous-time random walks on a multidimensional lattice with finite number of sources of particle generation of the same intensity without any constraint on the variance of jumps. For the evolution operator of the mean population size of particles with nearly critical source intensity, the asymptotic behavior of the Green function and of the eigenvalue is found. The effect of “limit coalescence” of eigenvalues is revealed for such an arrangement of sources that the distances between them go off to infinity.
Keywords: branching random walks, convolution-type operators, Green functions, multipoint perturbations, positive eigenvalues.
Funding agency Grant number
Russian Science Foundation 14-21-00162
This research was carried out with the financial support of the Russian Science Foundation (grant 14-21-00162).
Received: 16.05.2017
English version:
Theory of Probability and its Applications, 2018, Volume 62, Issue 3, Pages 413–431
DOI: https://doi.org/10.1137/S0040585X97T98871X
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: E. B. Yarovaya, “Spectral asymptotics of supercritical branching random process”, Teor. Veroyatnost. i Primenen., 62:3 (2017), 518–541; Theory Probab. Appl., 62:3 (2018), 413–431
Citation in format AMSBIB
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
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