On the maximal offspring in a critical branching process with infinite variance

Abstract : We investigate the maximal number $M_k$ of offsprings amongst all individuals in a critical Galton-Watson process started with $k$ ancestors. We show that when the reproduction law has a regularly varying tail with index $-\alpha$ for $1<\alpha<2$, then $k^{-1}M_k$ converges in distribution to a Frechet law with shape parameter $1$ and scale parameter depending only on $\alpha$.
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https://hal.archives-ouvertes.fr/hal-00515925
Contributor : Jean Bertoin <>
Submitted on : Wednesday, September 8, 2010 - 12:09:38 PM
Last modification on : Sunday, March 31, 2019 - 1:35:03 AM
Long-term archiving on: Tuesday, October 23, 2012 - 3:45:26 PM

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• HAL Id : hal-00515925, version 1

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Jean Bertoin. On the maximal offspring in a critical branching process with infinite variance. 2010. ⟨hal-00515925⟩

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