Email this article On the Mean Number of Particles of a Branching Random Walk on ℤd with Periodic Sources of Branching
- Authors: Platonova M.V.1, Ryadovkin K.S.1
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Affiliations:
- St. Petersburg State University
- Issue: Vol 97, No 2 (2018)
- Pages: 140-143
- Section: Mathematics
- URL: https://journal-vniispk.ru/1064-5624/article/view/225477
- DOI: https://doi.org/10.1134/S1064562418020102
- ID: 225477
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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 → ∞.
About the authors
M. V. Platonova
St. Petersburg State University
Author for correspondence.
Email: mariyaplat@rambler.ru
Russian Federation, St. Petersburg
K. S. Ryadovkin
St. Petersburg State University
Email: mariyaplat@rambler.ru
Russian Federation, St. Petersburg
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