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arXiv · 1210.0250

Fine asymptotics for the consistent maximal displacement of branching Brownian motion

Matthew I. Roberts
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Abstract

It is well-known that the maximal particle in a branching Brownian motion sits near $\sqrt2 t - \frac{3}{2\sqrt2}\log t$ at time $t$. One may then ask about the paths of particles near the frontier: how close can they stay to this critical curve? Two different approaches to this question have been developed. We improve upon the best-known bounds in each case, revealing new qualitative features including marked differences between the two approaches.

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Matthew I. Roberts. 2014-06-19. Fine asymptotics for the consistent maximal displacement of branching Brownian motion. https://arxiv.org/abs/1210.0250

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