On explosions in heavy-tailed branching random walks

DOI10.1214/12-AOP806zbMath1304.60093arXiv1102.0950MaRDI QIDQ373551

Neil Olver, Simon Griffiths, Omid Amini, Luc P. Devroye

Publication date: 17 October 2013

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

Full work available at URL: https://arxiv.org/abs/1102.0950

zbMATH Keywords

limit theoremheavy-tailed distributionbranching random walkexplosionGalton-Watson trees

Mathematics Subject Classification ID

Combinatorial probability (60C05) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Zero-one laws (60F20)

Related Items (10)

Local neighbourhoods for first-passage percolation on the configuration model ⋮ Asymptotic behaviour of heavy-tailed branching processes in random environments ⋮ Doubly stochastic Yule cascades. II: The explosion problem in the non-reversible case ⋮ Critical percolation and \(\mathrm{A + B \rightarrow 2A}\) dynamics ⋮ Tight fluctuations of weight-distances in random graphs with infinite-variance degrees ⋮ Explosion and linear transit times in infinite trees ⋮ Weighted distances in scale-free configuration models ⋮ Nonuniversality of weighted random graphs with infinite variance degree ⋮ Explosion in weighted hyperbolic random graphs and geometric inhomogeneous random graphs ⋮ Penalising transmission to hubs in scale-free spatial random graphs

Cites Work

• Limit distributions for minimal displacement of branching random walks
• The central limit theorem for the supercritical branching random walk, and related results
• Tightness for a family of recursion equations
• Minimal position and critical martingale convergence in branching random walks, and directed polymers on disordered trees
• Postulates for subadditive processes
• The first birth problem for an age-dependent branching process
• Seneta-Heyde norming in the branching random walk
• Minimal positions in a branching random walk
• Branching processes. II
• Minima in branching random walks
• Necessary condition for the regularity of branching processes
• A note on some results of Schuh
• Sufficient Conditions for Regularity of Bellman–Harris Branching Processes
• A note on explosiveness of Markov branching processes
• Sums of i.i.d. random variables and an application to the explosion criterion for markov branching processes
• Almost sure convergence of branching processes
• Minimal displacement of branching random walk
• Foundations of Modern Probability
• Limit theorems for the minimal position in a branching random walk with independent logconcave displacements
• Functional equations and the Galton-Watson process
• The Galton-Watson process with infinite mean
• The simple branching process with infinite mean. I
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: On explosions in heavy-tailed branching random walks