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

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.