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arXiv · 1201.1701

An ergodic theorem for the frontier of branching Brownian motion

Louis-Pierre Arguin·Anton Bovier·Nicola Kistler
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Abstract

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)].

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Louis-Pierre Arguin, Anton Bovier, Nicola Kistler. 2012-01-09. An ergodic theorem for the frontier of branching Brownian motion. https://arxiv.org/abs/1201.1701

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