Geodesic
On the Maximum of a Branching Process Conditioned on the Total Progeny
Serdica Mathematical Journal, Tome 25 (1999) no. 2, pp. 141-176 Cet article a éte moissonné depuis la source Bulgarian Digital Mathematics Library

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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.
Keywords: Bienaymé-Galton-Watson Branching Process, Maximum, Total Progeny, Left-Continuous Random Walk, Random Rooted Labeled Trees 
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     title = {On the {Maximum} of a {Branching} {Process} {Conditioned} on the {Total} {Progeny}},
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Kerbashev, Tzvetozar. On the Maximum of a Branching Process Conditioned on the Total Progeny. Serdica Mathematical Journal, Tome 25 (1999) no. 2, pp. 141-176. http://geodesic.mathdoc.fr/item/SMJ2_1999_25_2_a4/