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

Marc Arnaudon, Abdoulaye Koléhè Coulibaly-Pasquier () and Laurent Miclo
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Marc Arnaudon: Équipe Calcul scientifique et Modélisation - IMB - Institut de Mathématiques de Bordeaux - UB - Université de Bordeaux - Bordeaux INP - Institut Polytechnique de Bordeaux - CNRS - Centre National de la Recherche Scientifique
Abdoulaye Koléhè Coulibaly-Pasquier: IECL - Institut Élie Cartan de Lorraine - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique
Laurent Miclo: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CNRS - Centre National de la Recherche Scientifique

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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.

Keywords: Spherical Brownian motions; Strong stationary times; Separation discrepancy; Hitting times; Small noise one-dimensional diffusions (search for similar items in EconPapers)
Date: 2024-04-30
Note: View the original document on HAL open archive server: https://hal.science/hal-04564247v1
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