Journal of Applied Probability

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

Jean Bertoin

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We investigate the maximal number Mk of offspring 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 -α for 1 < α < 2, then k-1Mk converges in distribution to a Frechet law with shape parameter 1 and scale parameter depending only on α.

Article information

J. Appl. Probab., Volume 48, Number 2 (2011), 576-582.

First available in Project Euclid: 21 June 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Branching process maximal offspring Frechet distribution stable Lévy process extreme value theory


Bertoin, Jean. On the maximal offspring in a critical branching process with infinite variance. J. Appl. Probab. 48 (2011), no. 2, 576--582. doi:10.1239/jap/1308662646.

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