@techreport{publications48678,
          volume = {24-1510},
           month = {February},
          author = {Marc Arnaudon and Abdoulaye Kol{\'e}h{\`e} Coulibaly-Pasquier and Laurent Miclo},
          series = {TSE Working Paper},
       booktitle = {TSE Working Paper},
            type = {Working Paper},
         address = {Toulouse},
           title = {On the separation cut-off phenomenon for Brownian motions on high dimensional spheres},
       publisher = {TSE Working Paper},
            year = {2024},
     institution = {Universit{\'e} Toulouse Capitole},
             url = {https://publications.ut-capitole.fr/id/eprint/48678/},
        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. 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.}
}