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Maximal displacement of branching brownian motion
Author(s) -
Bramson Maury D.
Publication year - 1978
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160310502
Subject(s) - mathematics , brownian motion , branching (polymer chemistry) , displacement (psychology) , dimension (graph theory) , position (finance) , branching random walk , mathematical analysis , mathematical physics , combinatorics , random walk , statistics , psychology , materials science , finance , economics , composite material , psychotherapist
It is shown that the position of any fixed percentile of the maximal displacement of standard branching Brownian motion in one dimension is 2 1/2 t–3 · 2 −3/2 log t + O (1) at time t , the second‐order term having been previously unknown. This determines (to within O (1)) the position of the travelling wave of the semilinear heat equation, u t =1/2 u xx + f ( u ), in the classic paper by Kolmogorov‐Petrovsky‐Piscounov, “ Étude de l'équations de la diffusion avec croissance de la quantité de la matière et son application à un problème biologique” , 1937.