@article{EJP2082,
author = {Louis-Pierre Arguin and Anton Bovier and Nicola Kistler},
title = {An ergodic theorem for the frontier of branching Brownian motion},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {18},
year = {2013},
keywords = {Branching Brownian motion, ergodicity, extreme value theory, KPP equation and traveling waves},
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, 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)].
},
pages = {no. 53, 1-25},
issn = {1083-6489},
doi = {10.1214/EJP.v18-2082},
url = {http://ejp.ejpecp.org/article/view/2082}}