Geodesic
Asymptotic behavior of the mean number of particles of branching random walk on $\mathbf Z^d$ with periodic sources of branching
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 26, Tome 466 (2017), pp. 234-256 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a continuous-time branching random walk on $\mathbf Z^d$ with birth and death of particles at a periodic set of points (the sources of branching). Spectral properties of an evolution operator of the mean number of particles are studied. We derive a representation of the mean value of particle number in a form of asymptotic series. 
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     title = {Asymptotic behavior of the mean number of particles of branching random walk on $\mathbf Z^d$ with periodic sources of branching},
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M. V. Platonova; K. S. Ryadovkin. Asymptotic behavior of the mean number of particles of branching random walk on $\mathbf Z^d$ with periodic sources of branching. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 26, Tome 466 (2017), pp. 234-256. http://geodesic.mathdoc.fr/item/ZNSL_2017_466_a15/

[1] E. A. Antonenko, E. B. Yarovaya, “Raspolozhenie sobstvennykh znachenii v spektre evolyutsionnogo operatora v vetvyaschemsya sluchainom bluzhdanii”, Sovremennye problemy matematiki i mekhaniki, 10:3 (2015), 9–22

[2] M. Sh. Birman, M. Z. Solomyak, Spektralnaya teoriya samosopryazhennykh operatorov v gilbertovom prostranstve, LGU, 1980 | MR

[3] I. I. Gikhman, A. V. Skorokhod, Vvedenie v teoriyu sluchainykh protsessov, Nauka, M., 1977 | MR

[4] B. A. Sevastyanov, Vetvyaschiesya protsessy, Nauka, M., 1971 | MR

[5] M. V. Fedoryuk, Metod perevala, Nauka, M., 1977 | MR

[6] E. B. Yarovaya, Vetvyaschiesya sluchainye bluzhdaniya v neodnorodnoi srede, Izd-vo TsPI pri mekhaniko-matematicheskom fakultete MGU, M., 2007

[7] E. B. Yarovaya, “Kriterii eksponentsialnogo rosta chisla chastits v modelyakh vetvyaschikhsya sluchainykh bluzhdanii”, Teoriya veroyatn. i ee primen., 55:4 (2010), 705–731 | DOI | MR

[8] E. B. Yarovaya, “Spektralnye svoistva evolyutsionnykh operatorov v modelyakh vetvyaschikhsya sluchainykh bluzhdanii”, Matem. zametki, 92:1 (2012), 123–140 | DOI | MR | Zbl

[9] P. R. Halmos, V. S. Sunder, Bounded Integral Operators on $L^2$ Spaces, Results in Mathematics and Related Areas, 96, Springer Science Business Media, 2012 | MR

[10] Y. Higuchi, Y. Nomura, “Spectral structure of the Laplacian on a covering graph”, Europ. J. Combin., 30:2 (2009), 570–585 | DOI | MR | Zbl

[11] Y. Higuchi, T. Shirai, “Some spectral and geometric properties for infinite graphs”, Contemporary Math., 347 (2004), 2–56 | MR

[12] R. A. Horn, C. R. Johnson, Matrix Analysis, Cambridge university press, 2012 | MR

[13] E. Korotyaev, N. Saburova, “Schrödinger operators on periodic discrete graphs”, J. Math. Analysis Appl., 420:1 (2014), 576–611 | DOI | MR | Zbl

[14] E. Korotyaev, N. Saburova, “Schrödinger operators with guided potentials on periodic graphs”, Proc. Amer. Math. Soc., 145:11 (2017), 4869–4883 | MR | Zbl

[15] M. Reed, B. Simon, Analysis of Operators, v. IV, Elsevier, 1978

[16] P. W. Sy, T. Sunada, “Discrete Schrödinger operators on a graph”, Nagoya Math. J., 125 (1992), 141–150 | DOI | MR | Zbl