{"title":"Propagation of the Front of Random Walk with Periodic Branching Sources","authors":"E. Vl. Bulinskaya","doi":"10.3103/s0027132224700049","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We consider the model of branching random walk on an integer lattice <span>\\(\\mathbb{Z}^{d}\\)</span> with periodic sources of branching. It is supposed that the regime of branching is supercritical and the Cramér condition is satisfied for a jump of the random walk. The theorem established describes the rate of front propagation for particles population over the lattice as the time increases unboundedly. The proofs are based on fundamental results related to the spatial spread of general branching random walk.</p>","PeriodicalId":42963,"journal":{"name":"Moscow University Mathematics Bulletin","volume":"28 1","pages":""},"PeriodicalIF":0.2000,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Moscow University Mathematics Bulletin","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3103/s0027132224700049","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We consider the model of branching random walk on an integer lattice \(\mathbb{Z}^{d}\) with periodic sources of branching. It is supposed that the regime of branching is supercritical and the Cramér condition is satisfied for a jump of the random walk. The theorem established describes the rate of front propagation for particles population over the lattice as the time increases unboundedly. The proofs are based on fundamental results related to the spatial spread of general branching random walk.
期刊介绍：
Moscow University Mathematics Bulletin is the journal of scientific publications reflecting the most important areas of mathematical studies at Lomonosov Moscow State University. The journal covers research in theory of functions, functional analysis, algebra, geometry, topology, ordinary and partial differential equations, probability theory, stochastic processes, mathematical statistics, optimal control, number theory, mathematical logic, theory of algorithms, discrete mathematics and computational mathematics.
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