Most trees are short and fat
成果类型：
Article
署名作者：
Addario-Berry, Louigi
署名单位：
McGill University
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-018-0829-x
发表日期：
2019
页码：
1-26
关键词：
摘要：
This work proves new probability bounds relating to the height, width, and size of Galton-Watson trees. For example, if T is any Galton-Watson tree, and H, W, and |T| are the height, width, and size of T, respectively, then H/W has sub-exponential tails and H/|T|1/2 has sub-Gaussian tails. Although our methods apply without any assumptions on the offspring distribution, when information is provided about the distribution the method can be adapted accordingly, and always seems to yield tight bounds.