The precise tail behavior of the total progeny of a killed branching random walk

DOI10.1214/13-AOP842zbMath1288.60105arXiv1102.5536MaRDI QIDQ2434906

Olivier Zindy, Yue Yun Hu, Elie E. F. Aidekon

Publication date: 31 January 2014

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1102.5536

zbMATH Keywords

killed branching random walktotal progenyspinal decompositiontime reversed random walkYaglom-type theorem

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items (8)

An Application of the Backbone Decomposition to Supercritical Super-Brownian Motion with a Barrier ⋮ From transience to recurrence with Poisson tree frogs ⋮ Predator-prey dynamics on infinite trees: a branching random walk approach ⋮ A strong law of large numbers for super-critical branching Brownian motion with absorption ⋮ The critical barrier for the survival of branching random walk with absorption ⋮ Number of particles absorbed in a BBM on the extinction event ⋮ Rank dependent branching-selection particle systems ⋮ Total number of births on the negative half-line of the binary branching Brownian motion in the boundary case

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Time reversal of random walks in one dimension
• Tail asymptotics for the total progeny of the critical killed branching random walk
• Total progeny in killed branching random walk
• Local probabilities for random walks conditioned to stay positive
• Minimal position and critical martingale convergence in branching random walks, and directed polymers on disordered trees
• On tails of fixed points of the smoothing transform in the boundary case
• General branching processes as Markov fields
• Random difference equations and renewal theory for products of random matrices
• Postulates for subadditive processes
• The first birth problem for an age-dependent branching process
• Inequalities for the overshoot
• On generalized multiplicative cascades
• Conceptual proofs of \(L\log L\) criteria for mean behavior of branching processes
• On conditioning a random walk to stay nonnegative
• The critical barrier for the survival of branching random walk with absorption
• The number of absorbed individuals in branching Brownian motion with a barrier
• The genealogy of branching Brownian motion with absorption
• Minima in branching random walks
• Implicit Renewal Theory and Power Tails on Trees
• Moments of ladder heights in random walks
• On the convergence of supercritical general (C-M-J) branching processes
• The first- and last-birth problems for a multitype age-dependent branching process
• Martingale convergence in the branching random walk
• Measure change in multitype branching
• On Excess Over the Boundary
• Extreme Values in the GI/G/1 Queue

This page was built for publication: The precise tail behavior of the total progeny of a killed branching random walk