Sam Olesker-Taylor

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math.PR2025

Cutoff for Almost All Random Walks on Abelian Groups

Jonathan Hermon, Sam Olesker-Taylor

Consider the random Cayley graph of a finite group $G$ with respect to $k$ generators chosen uniformly at random, with $1 ≪ lo g k ≪ lo g ∣ G ∣$ ; denote it $G_{k}$ . A conjecture of…

math.PR2025

Geometry of Random Cayley Graphs of Abelian Groups

Jonathan Hermon, Sam Olesker-Taylor

Consider the random Cayley graph of a finite Abelian group $G$ with respect to $k$ generators chosen uniformly at random, with $1 ≪ lo g k ≪ lo g ∣ G ∣$ . Draw a vertex $U \sim \o…

math.PR2025

Limit Profiles for Reversible Markov Chains

Evita Nestoridi, Sam Olesker-Taylor

In a recent breakthrough, Teyssier [Tey20] introduced a new method for approximating the distance from equilibrium of a random walk on a group. He used it to study the limit profil…

math.PR2025

Catalan percolation

Eleanor Archer, Ivailo Hartarsky, Brett Kolesnik +3

In Catalan percolation, all nearest-neighbor edges ${i, i + 1}$ along $Z$ are initially occupied, and all other edges are open independently with probability $p$ . Open edges…

math.PR2024

Time-Biased Random Walks and Robustness of Expanders

Sam Olesker-Taylor, Thomas Sauerwald, John Sylvester

Random walks on expanders play a crucial role in Markov Chain Monte Carlo algorithms, derandomization, graph theory, and distributed computing. A desirable property is that they ar…

math.PR2024

Limit Profile for Projections of Random Walks on Groups

Evita Nestoridi, Sam Olesker-Taylor

Establishing cutoff, an abrupt transition from "not mixed" to "well mixed", is a classical topic in the theory of mixing times for Markov chains. Interest has grown recently in det…