Branching Brownian motion: Almost sure growth along unscaled paths

Details Branching Brownian motion: Almost sure growth along unscaled paths Branching Brownian motion: Almost sure growth along unscaled paths

2008-11-11

arxiv.org/abs/0811.1704v1

Mathematics

Probability

20 pages, 2 figures

Scientific paper

We give new results on the growth of the number of particles in a dyadic branching Brownian motion which follow within a fixed distance of a path $f:[0,\infty)\to \mathbb{R}$. We show that it is possible to count the number of particles without rescaling the paths. Our results reveal that the number of particles along certain paths can oscillate dramatically. The methods used are entirely probabilistic, taking advantage of the spine technique developed by, amongst others, Lyons et al, Kyprianou, and Hardy & Harris.

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