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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
Sinaĭ excursions: An analogue of Sparre Andersen's formula for the area process of a random walk
Serte Donderwinkel, Brett Kolesnik
Sinaĭ 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 as…
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/n^…