The Annals of Probability

Convergence in law of the minimum of a branching random walk

Elie Aïdékon

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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.

Article information

Source
Ann. Probab., Volume 41, Number 3A (2013), 1362-1426.

Dates
First available in Project Euclid: 29 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aop/1367241502

Digital Object Identifier
doi:10.1214/12-AOP750

Mathematical Reviews number (MathSciNet)
MR3098680

Zentralblatt MATH identifier
1285.60086

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

Keywords
Minimum branching random walk killed branching random walk

Citation

Aïdékon, Elie. Convergence in law of the minimum of a branching random walk. Ann. Probab. 41 (2013), no. 3A, 1362--1426. doi:10.1214/12-AOP750. https://projecteuclid.org/euclid.aop/1367241502


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References

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