Sharp concentration for the largest and smallest fragment in a \(k\)-regular self-similar fragmentation

DOI10.1214/21-AOP1556zbMath1498.60315arXiv2102.08935MaRDI QIDQ2135402

Joscha Prochno, Nina Gantert, Piotr Dyszewski, Dominik Schmid, Samuel Johnston

Publication date: 6 May 2022

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

Full work available at URL: https://arxiv.org/abs/2102.08935

zbMATH Keywords

point processfragmentationbranching random walk

Mathematics Subject Classification ID

Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Continuous-time Markov processes on discrete state spaces (60J27) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Behavior near the extinction time in self-similar fragmentations. II: Finite dislocation measures.
• Asymptotics of self-similar growth-fragmentation processes
• Behavior near the extinction time in self-similar fragmentations. I: The stable case
• Extreme value theory for moving average processes
• Splitting intervals. II: Limit laws for lengths
• The asymptotic behavior of fragmentation processes
• Self-similar fragmentations
• The largest fragment of a homogeneous fragmentation process
• Ranked Fragmentations
• An Introduction to the Theory of Point Processes
• Discounted branching random walks
• Lectures on the Poisson Process
• On a Theorem of Breiman and a Class of Random Difference Equations
• Splitting intervals
• Homogeneous fragmentation processes

This page was built for publication: Sharp concentration for the largest and smallest fragment in a \(k\)-regular self-similar fragmentation