An ergodic theorem for the frontier of branching Brownian motion

Louis-Pierre Arguin (CIRM & Université Aix Marseille)
Anton Bovier (Universität Bonn)
Nicola Kistler (Universität Bonn)


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, distribtion 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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Pages: 1-25

Publication Date: May 13, 2013

DOI: 10.1214/EJP.v18-2082


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