Bienaymé-Galton-Watson Branching Process Maximum Total Progeny Left-Continuous Random Walk Random Rooted Labeled Trees
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 25, No 2, (1999), 141p-176p
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.