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math.PR2025

SinaÄ­ excursions: An analogue of Sparre Andersen's formula for the area process of a random walk

Serte Donderwinkel, Brett Kolesnik

SinaÄ­ initiated the study of random walks with persistently positive area processes, motivated by shock waves in solutions to the inviscid Burgers' equation. We find the precise a…

math.PR2024

Critical beta-splitting, via contraction

Brett Kolesnik

The critical beta-splitting tree, introduced by Aldous, is a Markov branching phylogenetic tree. Aldous and Pittel recently proved, amongst other results, a central limit theorem f…

math.PR2024

Tournaments and random walks

Serte Donderwinkel, Brett Kolesnik

We study the relationship between tournaments and random walks. This connection was first observed by Erdős and Moser. Winston and Kleitman came close to showing that $S_n=Θ(4^n/…