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2013 An ergodic theorem for the frontier of branching Brownian motion
Louis-Pierre Arguin, Anton Bovier, Nicola Kistler
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Electron. J. Probab. 18: 1-25 (2013). DOI: 10.1214/EJP.v18-2082


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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Louis-Pierre Arguin. Anton Bovier. Nicola Kistler. "An ergodic theorem for the frontier of branching Brownian motion." Electron. J. Probab. 18 1 - 25, 2013.


Accepted: 13 May 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1286.60082
MathSciNet: MR3065863
Digital Object Identifier: 10.1214/EJP.v18-2082

Primary: 60J80
Secondary: 60G70 , 82B44

Keywords: Branching Brownian motion , ergodicity , Extreme value theory , KPP equation and traveling waves

Vol.18 • 2013
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