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The structure of the positive discrete spectrum of the evolution operator arising in branching random walks

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Abstract

A branching random walk (BRW) with continuous time and a finite number of branching sources located at points of a multidimensional lattice is considered. The definition of weakly supercritical BRWs, whose discrete spectrum contains a unique positive eigenvalue, is introduced. Conditions for a supercritical BRW to be weakly supercritical are determined.

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Authors and Affiliations

  1. Mechanics and Mathematics Faculty, Moscow State University, Moscow, 119991, Russia

    E. B. Yarovaya

  2. Steklov Institute of Mathematics, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    E. B. Yarovaya

Authors
  1. E. B. Yarovaya
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Correspondence to E. B. Yarovaya.

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Original Russian Text © E.B. Yarovaya, 2015, published in Doklady Akademii Nauk, 2015, Vol. 463, No. 6, pp. 646–649.

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Yarovaya, E.B. The structure of the positive discrete spectrum of the evolution operator arising in branching random walks. Dokl. Math. 92, 507–510 (2015). https://doi.org/10.1134/S1064562415040316

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  • DOI: https://doi.org/10.1134/S1064562415040316

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