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arXiv · 2207.06052

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

Marc Arnaudon·Koléhé Abdoulaye Coulibaly-Pasquier·Laurent Miclo
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Abstract

This note proves that the separation convergence towards 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 a privious article by the authors to deduce the wanted cut-off phenomenon.

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Marc Arnaudon, Koléhé Abdoulaye Coulibaly-Pasquier, Laurent Miclo. 2022-07-13. On the separation cut-off phenomenon for Brownian motions on high dimensional spheres. https://arxiv.org/abs/2207.06052

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