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Recursive self-similarity for random trees, random triangulations and Brownian excursion. (English) Zbl 0808.60017
Author’s summary: 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.

MSC:
60C05 Combinatorial probability
60B10 Convergence of probability measures
60J65 Brownian motion
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