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On the Maximum of a Branching Process Conditioned on the Total Progeny

Kerbashev, Tzvetozar — 1999

Serdica Mathematical Journal

The maximum M of a critical Bienaymé-Galton-Watson process conditioned on the total progeny N is studied. Imbedding of the process in a random walk is used. A limit theorem for the distribution of M as N → ∞ is proved. The result is trasferred to the non-critical processes. A corollary for the maximal strata of a random rooted labeled tree is obtained.

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