# Branching Brownian motion: Almost sure growth along unscaled paths

## ResearchSpace/Manakin Repository

 dc.contributor.author Harris, Simon en dc.contributor.author Roberts, M en dc.date.accessioned 2019-06-19T21:39:49Z en dc.date.issued 2008-11-11 en dc.identifier.citation Arxiv (0811.1704v1). 11 Nov 2008. 20 pages en dc.identifier.uri http://hdl.handle.net/2292/47249 en dc.description.abstract 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. en dc.relation.ispartof Arxiv en dc.rights Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. en dc.rights.uri https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm en dc.rights.uri https://arxiv.org/licenses/nonexclusive-distrib/1.0/license.html en dc.subject math.PR en dc.subject math.PR en dc.subject 60J80 en dc.title Branching Brownian motion: Almost sure growth along unscaled paths en dc.type Report en dc.rights.holder Copyright: The authors en pubs.author-url http://arxiv.org/abs/0811.1704v1 en dc.rights.accessrights http://purl.org/eprint/accessRights/OpenAccess en pubs.subtype Working Paper en pubs.elements-id 761974 en pubs.org-id Science en pubs.org-id Statistics en pubs.arxiv-id 0811.1704 en pubs.number 0811.1704v1 en pubs.record-created-at-source-date 2019-08-20 en
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