3 papers
math.PR2026
On the universality of fluctuations for the cover time
Nathanaël Berestycki, Jonathan Hermon, Lucas Teyssier
We consider random walks on finite vertex-transitive graphs 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
Nathanaël 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
Every cutoff profile is possible
Lucas Teyssier
We introduce fruit-inosculated-tree Markov chains. These chains have easily tunable parameters and are a good source of examples. In particular, we prove that every cutoff profile…