Genealogy and spatial distribution of the \(N\)-particle branching random walk with polynomial tails

DOI10.1214/22-EJP806MaRDI QIDQ2082704

Zsófia Talyigás, Matthew I. Roberts, Sarah Penington

Publication date: 4 October 2022

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.12424

zbMATH Keywords

selectionheavy-tailed distributiongenealogybranching random walkstar-shaped coalescent

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

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Cites Work

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• Speed and fluctuations of \(N\)-particle branching Brownian motion with spatial selection
• Brunet-Derrida particle systems, free boundary problems and Wiener-Hopf equations
• Large deviations for random walks under subexponentiality: The big-jump domain
• Postulates for subadditive processes
• The first birth problem for an age-dependent branching process
• The maximum of a branching random walk with semiexponential increments
• The genealogy of branching Brownian motion with absorption
• Brunet-Derrida behavior of branching-selection particle systems on the line
• Hydrodynamics of the \(N\)-BBM process
• The limiting process of \(N\)-particle branching random walk with polynomial tails
• Maxima of branching random walks
• The first- and last-birth problems for a multitype age-dependent branching process
• Global existence for a free boundary problem of Fisher–KPP type

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