%0 Journal Article %1 MR893913 %A Lalley, S. P. %A Sellke, T. %D 1987 %J Ann. Probab. %K Fisher-KPP branching_Brownian_motion %N 3 %P 1052--1061 %T A conditional limit theorem for the frontier of a branching Brownian motion %U http://projecteuclid.org/euclid.aop/1176992080 %V 15 %X We prove a weak limit theorem which relates the large time behavior of the maximum of a branching Brownian motion to the limiting value of a certain associated martingale. This exhibits the minimal velocity travelling wave for the KPP-Fisher equation as a translation mixture of extreme-value distributions. We also show that every particle in a branching Brownian motion has a descendant at the frontier at some time. A final section states several conjectures concerning a hypothesized stationary "standing wave of particles" process and the relationship of this process to branching Brownian motion. Primary Subjects: 60J60 Keywords: Branching Brownian motion; KPP-Fisher equation; travelling wave; extreme-value distribution

@article{MR893913, abstract = { We prove a weak limit theorem which relates the large time behavior of the maximum of a branching Brownian motion to the limiting value of a certain associated martingale. This exhibits the minimal velocity travelling wave for the KPP-Fisher equation as a translation mixture of extreme-value distributions. We also show that every particle in a branching Brownian motion has a descendant at the frontier at some time. A final section states several conjectures concerning a hypothesized stationary "standing wave of particles" process and the relationship of this process to branching Brownian motion. Primary Subjects: 60J60 Keywords: Branching Brownian motion; KPP-Fisher equation; travelling wave; extreme-value distribution}, added-at = {2009-10-07T22:28:31.000+0200}, author = {Lalley, S. P. and Sellke, T.}, biburl = {https://www.bibsonomy.org/bibtex/2835f2378209f3824ee76729fb6ddc9f0/peter.ralph}, coden = {APBYAE}, fjournal = {The Annals of Probability}, interhash = {65702aeef6b8323fad6c24941a001596}, intrahash = {835f2378209f3824ee76729fb6ddc9f0}, issn = {0091-1798}, journal = {Ann. Probab.}, keywords = {Fisher-KPP branching_Brownian_motion}, mrclass = {60J65 (60J80)}, mrnumber = {MR893913 (88h:60161)}, mrreviewer = {Luis G. Gorostiza}, number = 3, pages = {1052--1061}, timestamp = {2012-04-23T01:33:35.000+0200}, title = {A conditional limit theorem for the frontier of a branching {B}rownian motion}, url = {http://projecteuclid.org/euclid.aop/1176992080}, volume = 15, year = 1987 }