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On the Mean Number of Particles of a Branching Random Walk on ℤd with Periodic Sources of Branching

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Abstract

We consider a continuous-time branching random walk on ℤd, where the particles are born and die on a periodic set of points (sources of branching). The spectral properties of the evolution operator for the mean number of particles at an arbitrary point of ℤd are studied. This operator is proved to have a positive spectrum, which leads to an exponential asymptotic behavior of the mean number of particles as t → ∞.

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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    M. V. Platonova & K. S. Ryadovkin

Authors
  1. M. V. Platonova
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  2. K. S. Ryadovkin
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Correspondence to M. V. Platonova.

Additional information

Original Russian Text © M.V. Platonova, K.S. Ryadovkin, 2018, published in Doklady Akademii Nauk, 2018, Vol. 479, No. 3, pp. 250–253.

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Platonova, M.V., Ryadovkin, K.S. On the Mean Number of Particles of a Branching Random Walk on ℤd with Periodic Sources of Branching. Dokl. Math. 97, 140–143 (2018). https://doi.org/10.1134/S1064562418020102

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  • DOI: https://doi.org/10.1134/S1064562418020102

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