### 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.
Keywords: Minimum; branching random walk; killed branching random walk

Original language | English |
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Pages (from-to) | 1362-1426 |

Number of pages | 65 |

Journal | The Annals of Probability |

Volume | 41 |

Issue number | 3A |

DOIs | |

Publication status | Published - 2013 |

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## Cite this

Aidékon, E. F. (2013). Convergence in law of the minimum of a branching random walk.

*The Annals of Probability*,*41*(3A), 1362-1426. https://doi.org/10.1214/12-AOP750