On the maximal displacement of critical branching random walk

DOI10.1007/s00440-014-0566-8zbMath1316.60132arXiv1212.2933OpenAlexW2068426901MaRDI QIDQ2349144

Yuan Shao, Steven P. Lalley

Publication date: 19 June 2015

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.2933

zbMATH Keywords

Feynman-Kac formulabranching random walkcritical branching processmaximal displacement

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Large deviations (60F10) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items (9)

Large deviation principle for the maximal positions in critical branching random walks with small drifts ⋮ Maximal displacement of spectrally negative branching Lévy processes ⋮ Unnamed Item ⋮ Convergence in law for the capacity of the range of a critical branching random walk ⋮ Critical branching Brownian motion with absorption: particle configurations ⋮ On the maximal displacement of catalytic branching random walk ⋮ On the maximal displacement of subcritical branching random walks ⋮ Lower deviation and moderate deviation probabilities for maximum of a branching random walk ⋮ On the maximal displacement of near-critical branching random walks

Cites Work

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• Branching Brownian motion seen from its tip
• The extremal process of branching Brownian motion
• Tail asymptotics for the total progeny of the critical killed branching random walk
• Critical branching random walks with small drift
• Tightness for a family of recursion equations
• A conditional limit theorem for the frontier of a branching Brownian motion
• Markov chains indexed by trees
• Branching random walks with acritical branching part
• Spatial epidemics: Critical behavior in one dimension
• Measure-valued Markov branching processes conditioned on non-extinction
• Genealogy of extremal particles of branching Brownian motion
• Application of brownian motion to the equation of kolmogorov-petrovskii-piskunov
• Martingale convergence in the branching random walk
• Maximal displacement of branching brownian motion
• The dispersion of a neutral allele considered as a branching process
• Maximum geographic range of a mutant allele considered as a subtype of a Brownian branching random field
• Limit theorems for the minimal position in a branching random walk with independent logconcave displacements

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