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An ergodic theorem for the frontier of branching Brownian motion


 
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1. Title Title of document An ergodic theorem for the frontier of branching Brownian motion
 
2. Creator Author's name, affiliation, country Louis-Pierre Arguin; CIRM & Université Aix Marseille; Canada
 
2. Creator Author's name, affiliation, country Anton Bovier; Universität Bonn; Germany
 
2. Creator Author's name, affiliation, country Nicola Kistler; Universität Bonn; Germany
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Branching Brownian motion, ergodicity, extreme value theory, KPP equation and traveling waves
 
3. Subject Subject classification 60J80; 60G70; 82B44
 
4. Description 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)].
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) German Research Foundation in the SFB 611, NSF, NSERC Canada and FQRNT Qu ebec.
 
7. Date (YYYY-MM-DD) 2013-05-13
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/2082
 
10. Identifier Digital Object Identifier 10.1214/EJP.v18-2082
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 18
 
12. Language English=en en
 
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