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.
Citation
David Aldous. "Recursive Self-Similarity for Random Trees, Random Triangulations and Brownian Excursion." Ann. Probab. 22 (2) 527 - 545, April, 1994. https://doi.org/10.1214/aop/1176988720
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