Tail bounds for the height and width of a random tree with a given degree sequence

@article{AddarioBerry2012TailBF,
title={Tail bounds for the height and width of a random tree with a given degree sequence},
author={L. Addario-Berry},
journal={Random Struct. Algorithms},
year={2012},
volume={41},
pages={253-261}
}

Fix a sequence c = (c1,…,cn) of non-negative integers with sum n − 1. We say a rooted tree T has child sequence c if it is possible to order the nodes of T as v1,…,vn so that for each 1 ≤ i ≤ n, vi has exactly ci children. Let \documentclass{article}\usepackage{mathrsfs}\usepackage{amsmath}\pagestyle{empty}\begin{document}${\mathcal T}$\end{document} **image** be a plane tree drawn uniformly at random from among all plane trees with child sequence c. In this note we prove sub-Gaussian tail… CONTINUE READING