Convergence in law of the minimum of a branching random walk

Details Convergence in law of the minimum of a branching random walk Convergence in law of the minimum of a branching random walk

2011-01-10

arxiv.org/abs/1101.1810v3

Mathematics

Probability

figures and details in some proofs added; proof of Lemma C.1 slightly changed. arXiv admin note: text overlap with arXiv:1107.

Scientific paper

We consider the minimum of a super-critical branching random walk. In
\cite{addario-berry-reed}, Addario-Berry and Reed 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 \cite{bramson83} in
the case of the branching Brownian motion.

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