%0 Report
%9 Working Paper
%A Arnaudon, Marc
%A Coulibaly-Pasquier, Abdoulaye Koléhè
%A Miclo, Laurent
%B TSE Working Paper
%C Toulouse
%D 2024
%F publications:48678
%I Université Toulouse Capitole
%T On the separation cut-off phenomenon for Brownian motions on high dimensional spheres
%U https://publications.ut-capitole.fr/id/eprint/48678/
%V 24-1510
%X 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. 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.