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Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2016, Number 2, Pages 37–40 (Mi vmumm134)  

Short notes

A weakly supercritical mode in a branching random walk

E. A. Antonenko

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The case of weakly supercritical branching random walks is considered. A theorem on asymptotic behavior of the eigenvalue of the operator defining the process is obtained for this case. Analogues of the theorems on asymptotic behavior of the Green function under large deviations of a branching random walk and asymptotic behavior of the spread front of population of particles are established for the case of a simple symmetric branching random walk over a many-dimensional lattice. The constants for these theorems are exactly determined in terms of parameters of walking and branching.

Key words: branching random walks, weakly supercritical case, Green function, spread front of population.

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English version:
Moscow University Mathematics Bulletin, 2016, 71:2, 68–70

Bibliographic databases:

UDC: 519.21
Received: 01.10.2014

Citation: E. A. Antonenko, “A weakly supercritical mode in a branching random walk”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2016, no. 2, 37–40; Moscow University Mathematics Bulletin, 71:2 (2016), 68–70

Citation in format AMSBIB
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