Fine asymptotics for the consistent maximal displacement of branching brownian motion

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Abstract

Ipt is well-known that the maximal particle in a branching Brownian motion sits near (Formula-Presented)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.

Original languageEnglish
Article number28
Pages (from-to)1-26
Number of pages26
JournalElectronic Journal of Probability
Volume20
DOIs
Publication statusPublished - 13 Mar 2015

Keywords

  • Branching Brownian motion
  • Consistent minimal displacement
  • Growth rate
  • Survival probability

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