RECURSIVE SELF-SIMILARITY FOR RANDOM TREES, RANDOM TRIANGULATIONS AND BROWNIAN EXCURSION

• 成果类型: Article
• 署名作者: ALDOUS, D
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176988720
• 发表日期: 1994
• 页码: 527-545
• 关键词: continuum random tree; fractals

摘要

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.