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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2013, Volume 282, Pages 195–211
DOI: https://doi.org/10.1134/S0371968513030163
(Mi tm3485)
 

This article is cited in 11 scientific papers (total in 12 papers)

Large deviations for a symmetric branching random walk on a multidimensional lattice

S. A. Molchanova, E. B. Yarovayab

a University of North Carolina, Charlotte, NC, USA
b Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
References:
Abstract: 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.
Received in November 2012
English version:
Proceedings of the Steklov Institute of Mathematics, 2013, Volume 282, Pages 186–201
DOI: https://doi.org/10.1134/S0081543813060163
Bibliographic databases:
Document Type: Article
UDC: 519.218.25
Language: Russian
Citation: S. A. Molchanov, E. B. Yarovaya, “Large deviations for a symmetric branching random walk on a multidimensional lattice”, Branching processes, random walks, and related problems, Collected papers. Dedicated to the memory of Boris Aleksandrovich Sevastyanov, corresponding member of the Russian Academy of Sciences, Trudy Mat. Inst. Steklova, 282, MAIK Nauka/Interperiodica, Moscow, 2013, 195–211; Proc. Steklov Inst. Math., 282 (2013), 186–201
Citation in format AMSBIB
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\by S.~A.~Molchanov, E.~B.~Yarovaya
\paper Large deviations for a~symmetric branching random walk on a~multidimensional lattice
\inbook Branching processes, random walks, and related problems
\bookinfo Collected papers. Dedicated to the memory of Boris Aleksandrovich Sevastyanov, corresponding member of the Russian Academy of Sciences
\serial Trudy Mat. Inst. Steklova
\yr 2013
\vol 282
\pages 195--211
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\pages 186--201
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  • https://doi.org/10.1134/S0371968513030163
  • https://www.mathnet.ru/eng/tm/v282/p195
  • This publication is cited in the following 12 articles:
    1. Xiaoyun Chen, Dan Han, Stanislav A. Molchanov, “Phase transitions in the non-stationary lattice Anderson model”, Journal of Mathematical Physics, 65:12 (2024)  crossref
    2. D. M. Balashova, E. B. Yarovaya, “Structure of the Population of Particles for a Branching Random Walk in a Homogeneous Environment”, Proc. Steklov Inst. Math., 316 (2022), 57–71  mathnet  crossref  crossref
    3. D. M. Balashova, “Clustering effect for multitype branching random walk”, Theory Probab. Appl., 67:3 (2022), 352–362  mathnet  crossref  crossref
    4. Iuliia Makarova, Daria Balashova, Stanislav Molchanov, Elena Yarovaya, “Branching Random Walks with Two Types of Particles on Multidimensional Lattices”, Mathematics, 10:6 (2022), 867  crossref
    5. Balashova D., Molchanov S., Yarovaya E., “Structure of the Particle Population For a Branching Random Walk With a Critical Reproduction Law”, Methodol. Comput. Appl. Probab., 23:1 (2021), 85–102  crossref  mathscinet  isi
    6. Feng Ya., Molchanov S., Yarovaya E., “Stability and Instability of Steady States For a Branching Random Walk”, Methodol. Comput. Appl. Probab., 23:1 (2021), 207–218  crossref  mathscinet  isi
    7. Random Motions in Markov and Semi‐Markov Random Environments 1, 2021, 205  crossref
    8. Yulia Makarova, Vladimir Kutsenko, Elena Yarovaya, Springer Proceedings in Mathematics & Statistics, 371, Recent Developments in Stochastic Methods and Applications, 2021, 255  crossref
    9. “Abstracts of talks given at the 4th International Conference on Stochastic Methods”, Theory Probab. Appl., 65:1 (2020), 121–172  mathnet  crossref  crossref  isi  elib
    10. D. M. Balashova, “Branching random walks with alternating sign intensities of branching sources”, J. Math. Sci., 262:4 (2022), 442–451  mathnet  crossref
    11. Molchanov S., Vainberg B., “Population Dynamics With Moderate Tails of the Underlying Random Walk”, SIAM J. Math. Anal., 51:3 (2019), 1824–1835  crossref  mathscinet  isi
    12. A. Grigor'yan, Yu. Kondratiev, A. Piatnitski, E. Zhizhina, “Pointwise estimates for heat kernels of convolution-type operators”, Proc. London Math. Soc., 117:4 (2018), 849–880  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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