Mathematics – Probability

Scientific paper

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2012-01-09

Mathematics

Probability

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Scientific paper

We prove a conjecture of Lalley and Sellke [Ann. Probab. 15 (1987)] asserting that the empirical (time-averaged) distribution function of the maximum of branching Brownian motion converges almost surely to a double exponential, or Gumbel, distribution with a random shift. The method of proof is based on the decorrelation of the maximal displacements for appropriate time scales. A crucial input is the localization of the paths of particles close to the maximum that was previously established by the authors [Comm. Pure Appl. Math. 64 (2011)].

**Arguin Louis-Pierre**

Mathematics – Probability

Scientist

**Bovier Anton**

Physics – Condensed Matter – Disordered Systems and Neural Networks

Scientist

**Kistler Nicola**

Physics – Mathematical Physics

Scientist

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