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

Laurent Miclo, Koléhè Coulibaly-Pasquier and Marc Arnaudon

No 24-1510, TSE Working Papers from Toulouse School of Economics (TSE)

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 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 [1] to deduce the wanted cut-off phenomenon

Date: 2024-02
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Persistent link: https://EconPapers.repec.org/RePEc:tse:wpaper:129124

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