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Teor. Veroyatnost. i Primenen., 2017, Volume 62, Issue 3, Pages 518–541 (Mi tvp5111)  

This article is cited in 4 scientific papers (total in 4 papers)

Spectral asymptotics of supercritical branching random process

E. B. Yarovaya

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

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).


DOI: https://doi.org/10.4213/tvp5111

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English version:
Theory of Probability and its Applications, 2018, 62:3, 413–431

Bibliographic databases:

Received: 16.05.2017

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

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Rytova A., Yarovaya E., “Survival Analysis of Particle Populations in Branching Random Walks”, Commun. Stat.-Simul. Comput.  crossref  isi
    2. E. B. Yarovaya, “Branching random walk with receding sources”, Russian Math. Surveys, 73:3 (2018), 549–551  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. A. I. Rytova, E. B. Yarovaya, “Moments of the numbers of particles in a heavy-tailed branching random walk”, Russian Math. Surveys, 74:6 (2019), 1126–1128  mathnet  crossref  crossref  isi
    4. I. Khristolyubov, E. B. Yarovaya, “A limit theorem for supercritical random branching walks with branching sources of varying intensity”, Theory Probab. Appl., 64:3 (2019), 365–384  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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