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Convergence of simple random walks on random discrete trees to Brownian motion on the continuum random tree
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Croydon, David A. (2008) Convergence of simple random walks on random discrete trees to Brownian motion on the continuum random tree. Annales de l'Institut Henri Poincaré (B). Probabilites et Statistiques, Vol.44 (No.6). pp. 987-1019. doi:10.1214/07-AIHP153 ISSN 0246-0203.
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Official URL: http://dx.doi.org/10.1214/07-AIHP153
Abstract
In this article it is shown that the Brownian motion on the continuum random tree is the scaling limit of the simple random walks on any family of discrete n-vertex ordered graph trees whose search-depth functions converge to the Brownian excursion as n --> infinity. We prove both a quenched version (for typical realisations of the trees) and in annealed version (averaged over all realisations of the trees) of our main result. The assumptions of the article cover the important example of simple random walks oil the trees generated by the Galton-Watson branching process. conditioned oil the total population size.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Library of Congress Subject Headings (LCSH): | Random walks (Mathematics), Trees (Graph theory), Brownian motion processes, Scaling laws (Statistical physics) | ||||
Journal or Publication Title: | Annales de l'Institut Henri Poincaré (B). Probabilites et Statistiques | ||||
Publisher: | Institute of Mathematical Statistics | ||||
ISSN: | 0246-0203 | ||||
Official Date: | December 2008 | ||||
Dates: |
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Volume: | Vol.44 | ||||
Number: | No.6 | ||||
Number of Pages: | 33 | ||||
Page Range: | pp. 987-1019 | ||||
DOI: | 10.1214/07-AIHP153 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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