An ergodic theorem for the frontier of branching Brownian motion
Probability
2012-01-10 v1
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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Cite
@article{arxiv.1201.1701,
title = {An ergodic theorem for the frontier of branching Brownian motion},
author = {Louis-Pierre Arguin and Anton Bovier and Nicola Kistler},
journal= {arXiv preprint arXiv:1201.1701},
year = {2012}
}
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4 figures