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math.PR2024
Tight universal bounds on the height times the width of random trees
Serte Donderwinkel, Robin Khanfir
We obtain assumption-free, non-asymptotic, uniform bounds on the product of the height and the width of uniformly random trees with a given degree sequence, conditioned Bienaymé tr…
math.PR2024
Fluctuations of the Horton-Strahler number of stable Galton-Watson trees
Robin Khanfir
The Horton-Strahler number -- also called the register function -- is a combinatorial tool that quantifies the branching complexity of a rooted tree. We study the law of the Horton…