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

被引：1

作者：

Arnaudon, Marc ^{[1
,2
]}

Coulibaly-pasquier, Kolehe ^{[3
,4
]}

Miclo, Laurent ^{[5
,6
,7
]}

机构：

[1] Univ Bordeaux, Inst Math Bordeaux, CNRS, Bordeaux, France

[2] INP Bordeaux, Bordeaux, France

[3] Univ Lorraine, Inst Elie Cartan Lorraine, Nancy, France

[4] CNRS, Nancy, France

[5] CNRS, Toulouse Sch Econ, Toulouse, France

[6] CNRS, Inst Math Toulouse, Toulouse, France

[7] Univ Toulouse, Toulouse, France

来源：

BERNOULLI | 2024年 / 30卷 / 02期

关键词：

Hitting times; separation discrepancy; small noise one-dimensional diffusions; spherical Brownian; motions; strong stationary times;

D O I：

10.3150/23-BEJ1622

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：1007 / 1028

页数：22

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