Scaling limits of random Polya trees

• 成果类型: Article
• 署名作者: Panagiotou, Konstantinos; Stufler, Benedikt
• 署名单位: University of Munich; Ecole Normale Superieure de Lyon (ENS de LYON)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-017-0770-4
• 发表日期: 2018
• 页码: 801-820
• 关键词: galton-watson; graphs

摘要

Polya trees are rooted trees considered up to symmetry. We establish the convergence of large uniform random Polya trees with arbitrary degree restrictions to Aldous' Continuum Random Tree with respect to the Gromov-Hausdorff metric. Our proof is short and elementary, and it is based on a novel decomposition: it shows that the global shape of a random Polya tree is essentially dictated by a large Galton-Watson tree that it contains. We also derive sub-Gaussian tail bounds for both the height and the width, which are optimal up to constant factors in the exponent.