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XII Symposium of Probability and Stochastic Processes pp 219–234Cite as

Birkhäuser

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

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Part of the book series: Progress in Probability ((PRPR,volume 73))

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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Acknowledgements

The authors would like to thank Fabian Freund for some very valuable comments. Arno Siri-Jégousse would like to welcome Raphaël Clodic Griffon, born the day the final version was sent. ASJ is supported by CONACyT Grant CB-2014/243068.

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Authors and Affiliations

  1. IIMAS, Universidad Nacional Autónoma de México, Mexico City, Mexico

    Arno Siri-Jégousse

  2. Department of Mathematical Sciences, Xi’an Jiaotong-Liverpool University, Suzhou, People’s Republic of China

    Linglong Yuan

Authors
  1. Arno Siri-Jégousse
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  2. Linglong Yuan
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Corresponding author

Correspondence to Arno Siri-Jégousse .

Editor information

Editors and Affiliations

  1. Department of Probability and Statistics, Center for Research in Mathematics, Guanajuato, Mexico

    Daniel Hernández-Hernández

  2. Department of Probability and Statistics, Center for Research in Mathematics, Guanajuato, Mexico

    Juan Carlos Pardo

  3. Department of Probability and Statistics, Center for Research in Mathematics, Guanajuato, Mexico

    Victor Rivero

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Siri-Jégousse, A., Yuan, L. (2018). A Note on the Small-Time Behaviour of the Largest Block Size of Beta n-Coalescents. In: Hernández-Hernández, D., Pardo, J., Rivero, V. (eds) XII Symposium of Probability and Stochastic Processes. Progress in Probability, vol 73. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-77643-9_8

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