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Scaling Limits of Markov-Branching Trees and Applications Read chapter Read first chapter

2018 | OriginalPaper | Chapter

A Note on the Small-Time Behaviour of the Largest Block Size of Beta n-Coalescents

Authors : Arno Siri-Jégousse, Linglong Yuan

Published in: XII Symposium of Probability and Stochastic Processes

Publisher: Springer International Publishing

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Abstract

We study the largest block size of Beta n-coalescents at small times as n tends to infinity, using the paintbox construction of Beta-coalescents and the link between continuous-state branching processes and Beta-coalescents established in Birkner et al. (Electron J Probab 10(9):303–325, 2005) and Berestycki et al. (Ann Inst H Poincaré Probab Stat 44(2):214–238, 2008). As a corollary, a limit result on the largest block size at the coalescence time of the individual/block {1} is provided.

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previous chapter A Criterion for Blow Up in Finite Time of a System of 1-Dimensional Reaction-Diffusion Equations
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Metadata
Title
A Note on the Small-Time Behaviour of the Largest Block Size of Beta n-Coalescents
Authors
Arno Siri-Jégousse
Linglong Yuan
Copyright Year
2018
Book
XII Symposium of Probability and Stochastic Processes

Print ISBN: 978-3-319-77642-2

Electronic ISBN: 978-3-319-77643-9

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-77643-9_8