On the maximal offspring in a critical branching process with infinite variance
نویسنده
چکیده
We investigate the maximal numberMk 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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