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Critical trees are neither too short nor too fat
- Publication Year :
- 2023
-
Abstract
- We establish lower tail bounds for the height, and upper tail bounds for the width, of critical size-conditioned Bienaym\'e trees. Our bounds are optimal at this level of generality. We also obtain precise asymptotics for offspring distributions within the domain of attraction of a Cauchy distribution, under a local regularity assumption. Finally, we pose some questions on the possible asymptotic behaviours of the height and width of critical size-conditioned Bienaym\'e trees.<br />Comment: 30 pages
- Subjects :
- Mathematics - Probability
Mathematics - Combinatorics
05C05, 60C05, 60J80
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2311.06163
- Document Type :
- Working Paper