Convergence in law of the minimum of a branching random walk

Abstract

We consider the minimum of a super-critical branching random walk. Addario-Berry and Reed [Ann. Probab. 37 (2009) 1044-1079] 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 Bramson [Mem. Amer. Math. Soc. 44 (1983) iv+190] in the case of the branching Brownian motion.

Published in at http://dx.doi.org/10.1214/12-AOP750 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org) Compared to the published version, we extended our result to the case of an infinite number of children. To this end, we added Corollary 3.5 and slightly changed the proof of Theorem 1.1. arXiv admin note: text overlap with arXiv:1107.2543 by other authors

References in corpus (4)

• Minima in branching random walks
• Tightness for a family of recursion equations
• The Seneta--Heyde scaling for the branching random walk
• A Local Limit Theorem for random walks conditioned to stay positive

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