Asymptotic Behavior of Branching Random Walks on Some Two-Dimensional Lattices
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DOI: 10.1007/s10958-020-05074-8
Abstract: A branching random walk on two-dimensional lattices corresponding to graphene and stanene is considered. It is assumed that sources of branching are located on lattices periodically. An asymptotics of the mean value of particles in… read more here.
Keywords: asymptotic behavior; behavior branching; two dimensional; dimensional lattices ... See more keywords
Cover time for branching random walks on regular trees
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DOI: 10.1017/jpr.2021.46
Abstract: Abstract Let T be the regular tree in which every vertex has exactly $d\ge 3$ neighbours. Run a branching random walk on T, in which at each time step every particle gives birth to a… read more here.
Keywords: branching random; time; time branching; cover time ... See more keywords
Particle-number distribution in large fluctuations at the tip of branching random walks.
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DOI: 10.1103/physreve.102.022104
Abstract: We investigate properties of the particle distribution near the tip of one-dimensional branching random walks at large times t, focusing on unusual realizations in which the rightmost lead particle is very far ahead of its… read more here.
Keywords: number; random walks; distribution; particle number ... See more keywords
A revisited proof of the Seneta-Heyde norming for branching random walks under optimal assumptions
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DOI: 10.1214/19-ejp350
Abstract: We introduce a set of tools which simplify and streamline the proofs of limit theorems concerning near-critical particles in branching random walks under optimal assumptions. We exemplify our method by giving another proof of the… read more here.
Keywords: proof seneta; seneta heyde; optimal assumptions; random walks ... See more keywords