Publication: On the maximal offspring in a critical branching process with infinite mean
On the maximal offspring in a critical branching process with infinite mean
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Bertoin, J. (2011). On the maximal offspring in a critical branching process with infinite mean. Journal of Applied Probability, 48(2), 576–582. https://doi.org/10.1239/jap/1308662646
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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.
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- Bertoin, J
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Bertoin, J. (2011). On the maximal offspring in a critical branching process with infinite mean. Journal of Applied Probability, 48(2), 576–582. https://doi.org/10.1239/jap/1308662646
