Maximal displacement of branching brownian motion
Author:
- Maury D. BramsonMBMaury D. Bramson
- 1 September 1978
- journal article
- research article
- Published by Wiley in Communications on Pure and Applied Mathematics
- Vol. 31 (5) , 531-581
Abstract
It is shown that the position of any fixed percentile of the maximal displacement of standard branching Brownian motion in one dimension is 21/2t–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, ut =1/2uxx +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.Keywords
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