The Annals of Probability

Recursive Self-Similarity for Random Trees, Random Triangulations and Brownian Excursion

David Aldous

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Abstract

Recursive self-similarity for a random object is the property of being decomposable into independent rescaled copies of the original object. Certain random combinatorial objects--trees and triangulations--possess approximate versions of recursive self-similarity, and then their continuous limits possess exact recursive self-similarity. In particular, since the limit continuum random tree can be identified with Brownian excursion, we get a nonobvious recursive self-similarity property for Brownian excursion.

Article information

Source
Ann. Probab., Volume 22, Number 2 (1994), 527-545.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176988720

Digital Object Identifier
doi:10.1214/aop/1176988720

Mathematical Reviews number (MathSciNet)
MR1288122

Zentralblatt MATH identifier
0808.60017

JSTOR
links.jstor.org

Subjects
Primary: 60C05: Combinatorial probability
Secondary: 60B10: Convergence of probability measures 60J65: Brownian motion [See also 58J65]

Keywords
Self-similarity recursive random tree random triangulation Brownian excursion weak convergence centroid continuum tree

Citation

Aldous, David. Recursive Self-Similarity for Random Trees, Random Triangulations and Brownian Excursion. Ann. Probab. 22 (1994), no. 2, 527--545. doi:10.1214/aop/1176988720. https://projecteuclid.org/euclid.aop/1176988720


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