May 2024 On the separation cut-off phenomenon for Brownian motions on high dimensional spheres
Marc Arnaudon, Koléhè Coulibaly-Pasquier, Laurent Miclo
Author Affiliations +
Bernoulli 30(2): 1007-1028 (May 2024). DOI: 10.3150/23-BEJ1622

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.

Funding Statement

The third author was funded by the grant ANR-17-EURE-0010.

Citation

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Marc Arnaudon. Koléhè Coulibaly-Pasquier. Laurent Miclo. "On the separation cut-off phenomenon for Brownian motions on high dimensional spheres." Bernoulli 30 (2) 1007 - 1028, May 2024. https://doi.org/10.3150/23-BEJ1622

Information

Received: 1 July 2022; Published: May 2024
First available in Project Euclid: 31 January 2024

MathSciNet: MR4699543
Digital Object Identifier: 10.3150/23-BEJ1622

Keywords: hitting times , separation discrepancy , small noise one-dimensional diffusions , spherical Brownian motions , strong stationary times

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Vol.30 • No. 2 • May 2024
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