On the separation cut-off phenomenon for Brownian motions on high dimensional spheres

Abstract

This paper proves that the separation convergence toward the uniform distribution abruptly occurs at times around lnpnq{n for the (time-accelerated by 2) Brownian motion on the sphere with a high dimension n. The arguments are based on a new and elementary perturbative approach for estimating hitting times in a small noise context. The quantitative estimates thus obtained are applied to the strong stationary times constructed in [1] to deduce the wanted cut-off phenomenon

Replaced by

Marc Arnaudon, Koléhè Coulibaly-Pasquier, and Laurent Miclo, “On the separation cut-off phenomenon for Brownian motions on high dimensional spheres”, Bernoulli, 2024, forthcoming.

Reference

Marc Arnaudon, Koléhè Coulibaly-Pasquier, and Laurent Miclo, “On the separation cut-off phenomenon for Brownian motions on high dimensional spheres”, TSE Working Paper, n. 24-1510, February 2024.