| Título: | An ergodic theorem for the frontier of branching Brownian motion |
| Autores: |
Arguin, Louis-Pierre; CIRM & Université Aix Marseille Bovier, Anton; Universität Bonn Kistler, Nicola; Universität Bonn |
| Fecha: | 2013-01-04 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: | Peer-reviewed Article |
| Tema: |
Branching Brownian motion, ergodicity, extreme value theory, KPP equation and traveling waves 60J80; 60G70; 82B44 |
| Descripción: | 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)]. |
| Idioma: | Inglés |
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