Athreya, K. B. On the maximum sequence in a critical branching process. (English) Zbl 0643.60063 Ann. Probab. 16, No. 2, 502-507 (1988). Let \(\{Z_ n\}\) be a critical branching process in which the family size has finite variance. Let \(M_ n\) be the maximum population size up to the n th generation, so \(M_ n=\max \{Z_ j:0\leq j\leq n\}\). It is a consequence of results of A. G. Pakes [J. Appl. Probab. 24, 768-772 (1987; Zbl 0636.60047)] that, if \(Z_ 0=i\), lim sup(E(M\({}_ n)/\log n)\leq i\). Here it is shown that, if \(Z_ 0=i\), \(E(M_ n)/\log n\to i\) as \(n\to \infty\). Reviewer: J.Biggins Cited in 3 ReviewsCited in 10 Documents MSC: 60J80 Branching processes (Galton-Watson, birth-and-death, etc.) 60K99 Special processes Keywords:critical branching process; maximum population size Citations:Zbl 0636.60047 × Cite Format Result Cite Review PDF Full Text: DOI