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Waiting times for particles in a branching Brownian motion to reach the rightmost position. (English) Zbl 1291.60173

Summary: It has been proved by S. P. Lalley and T. Sellke [Ann. Probab. 15, 1052–1061 (1987; Zbl 0622.60085)] that every particle born in a branching Brownian motion has a descendant reaching the rightmost position at some future time. The main goal of the present paper is to estimate asymptotically as \(s\) goes to infinity, the first time that every particle alive at the time \(s\) has a descendant reaching the rightmost position.

MSC:

60J80 Branching processes (Galton-Watson, birth-and-death, etc.)

Citations:

Zbl 0622.60085
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References:

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