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

Marc Arnaudon (1) , Koléhé Abdoulaye Coulibaly-Pasquier (2) , Laurent Miclo (3)

1 IMB - Institut de Mathématiques de Bordeaux
2 IECL - Institut Élie Cartan de Lorraine
3 TSE-R - Toulouse School of Economics

This article 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 previous article by the authors to deduce the wanted cut-off phenomenon.

Mots clés: Strong stationary times; Separation discrepancy; Hitting times; Small noise one-dimensional diffusions; Spherical Brownian motions

Domaines: Probabilités [math.PR]

Marc Arnaudon, Koléhé Abdoulaye Coulibaly-Pasquier, Laurent Miclo. On the separation cut-off phenomenon for Brownian motions on high dimensional spheres. Bernoulli, inPress. ⟨hal-03715965⟩