J. Hermon

collaborators

7 papers

math.PR2026

On the universality of fluctuations for the cover time

NathanaÃ«l Berestycki, Jonathan Hermon, Lucas Teyssier

We consider random walks on finite vertex-transitive graphs $I^$ of bounded degree. We find a simple geometric condition which characterises the cover time fluctuations: the suitab…

math.PR2026

Stationary hitting times on vertex-transitive graphs

NathanaÃ«l Berestycki, Jonathan Hermon, Lucas Teyssier

We prove a refined version of the Aldous and Brown's exponential approximation of stationary hitting times. These are valid for all reversible Markov chains. We then specialise our…

math.PR2025

Covering a graph with independent walks

Jonathan Hermon, Perla Sousi

Let $P$ be an irreducible and reversible transition matrix on a finite state space $V$ with invariant distribution $I ¨ $ . We let $k$ chains start by choosing independent locations d…

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

Cutoff for random walk on random graphs with a community structure

Jonathan Hermon, AnÄela Å arkoviÄ, Perla Sousi

We consider a variant of the configuration model with an embedded community structure and study the mixing properties of a simple random walk on it. Every vertex has an internal $\…