Cutoff in separation profile for the flat torus, sphere, and projective spaces

TL;DR

This paper demonstrates that the cutoff phenomenon in the separation profile for Brownian motion on various symmetric spaces is characterized by the tail distribution of an explicit Gumbel distribution, using intertwining and dual processes.

Contribution

It establishes a precise description of the cutoff in separation profiles for Brownian motion on flat tori, spheres, and projective spaces, linking it to Gumbel distribution tails.

Findings

Cutoff in separation profile follows a Gumbel distribution tail.

Method involves intertwining and dual process representations.

Results apply to flat tori, spheres, and various projective spaces.

Abstract

In this paper we show that the cutoff in separation profile for Brownian motion on flat torus T n\,; on spheres S n\,; on real, complex and quaternionic projective space resp. P n pRq, P n pCq and P n pHq, is the tail distribution of some explicit Gumbel distribution. The proof is based on intertwining, dual process together with a representation formula of large moments of the covering time of the dual process.