Asymptotics of trees with a prescribed degree sequence and applications

@article{Broutin2014AsymptoticsOT,
title={Asymptotics of trees with a prescribed degree sequence and applications},
author={Nicolas Broutin and Jean-François Marckert},
journal={Random Struct. Algorithms},
year={2014},
volume={44},
pages={290-316}
}

Let t be a rooted tree and ni(t) the number of nodes in t having i children. The degree sequence (ni(t), i ≥ 0) of t satisfies ∑ i≥0 ni(t) = 1 + ∑ i≥0 ini(t) = |t|, where |t| denotes the number of nodes in t. In this paper, we consider trees sampled uniformly among all plane trees having the same degree sequence s; we write Ps for the corresponding distribution. Let s(κ) = (ni(κ), i ≥ 0) be a list of degree sequences indexed by κ corresponding to trees with size nκ → +∞. We show that under some… CONTINUE READING