Arnaudon, Marc, Coulibaly-Pasquier, Abdoulaye Koléhè and Miclo, LaurentORCID: https://orcid.org/0000-0001-5502-2862 (2024) On the separation cut-off phenomenon for Brownian motions on high dimensional spheres. Bernoulli, Vol. 30 (n° 2). pp. 1007-1028.

Abstract

This paper proves that the separation convergence toward the uniform distribution abruptly occurs at times around ln(n)∕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 (Arnaudon, Coulibaly-Pasquier and Miclo (2020)) to deduce the wanted cut-off phenomenon.