naa a22 4500 510812066 CHVBK 20180411083447.0 cr unu---uuuuu 180411e20131001xx s 000 0 eng 10.1134/S0081543813060163 doi (NATIONALLICENCE)springer-10.1134/S0081543813060163 Large deviations for a symmetric branching random walk on a multidimensional lattice [Elektronische Daten] [S. Molchanov, E. Yarovaya] An important role in the theory of branching random walks is played by the problem of the spectrum of a bounded symmetric operator, the generator of a random walk on a multidimensional integer lattice, with a one-point potential. We consider operators with potentials of a more general form that take nonzero values on a finite set of points of the integer lattice. The resolvent analysis of such operators has allowed us to study branching random walks with large deviations. We prove limit theorems on the asymptotic behavior of the Green function of transition probabilities. Special attention is paid to the case when the spectrum of the evolution operator of the mean numbers of particles contains a single eigenvalue. The results obtained extend the earlier studies in this field in such directions as the concept of a reaction front and the structure of a population inside a front and near its boundary. Pleiades Publishing, Ltd., 2013 Molchanov S. University of North Carolina at Charlotte, 9201 University City Blvd., 28223-0001, Charlotte, NC, USA aut Yarovaya E. Faculty of Mechanics and Mathematics, Moscow State University, 119991, Moscow, Russia aut Proceedings of the Steklov Institute of Mathematics Springer US; http://www.springer-ny.com 282/1(2013-10-01), 186-201 0081-5438 282:1<186 2013 282 11501 https://doi.org/10.1134/S0081543813060163 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1134/S0081543813060163 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Molchanov S. University of North Carolina at Charlotte, 9201 University City Blvd., 28223-0001, Charlotte, NC, USA aut NATIONALLICENCE 700 1- Yarovaya E. Faculty of Mechanics and Mathematics, Moscow State University, 119991, Moscow, Russia aut NATIONALLICENCE 773 0- Proceedings of the Steklov Institute of Mathematics Springer US; http://www.springer-ny.com 282/1(2013-10-01), 186-201 0081-5438 282:1<186 2013 282 11501 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer