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Convergence in law of the minimum of a branching random walk. (English) Zbl 1285.60086

Author’s abstract: We consider the minimum of a super-critical branching random walk. L. Addario-Berry and B. Reed [Ann. Probab. 37, No. 3, 1044–1079 (2009; Zbl 1196.60142)] proved the tightness of the minimum centered around its mean value. We show that a convergence in law holds, giving the analog of a well-known result of M. Bramson [Mem. Am. Math. Soc. 285, 190 p. (1983; Zbl 0517.60083)] in the case of the branching Brownian motion.

MSC:

60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
60F05 Central limit and other weak theorems

References:

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