Random walks in the high-dimensional limit II: The crinkled subordinator

被引：1

作者：

Kabluchko, Zakhar ^{[1
]}

Marynych, Alexander ^{[2
]}

Raschel, Kilian ^{[3
]}

机构：

[1] Westfal Wilhelms Univ Munster, Inst Math Stochast, Munster, Germany

[2] Taras Shevchenko Natl Univ, Fac Comp Sci & Cybernet, Kyiv, Ukraine

[3] Univ Angers, Lab Angevin Rech Math, CNRS, Angers, France

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2024年 / 176卷

基金：

欧洲研究理事会;

关键词：

Crinkled arc; Gromov-Hausdorff convergence; Hausdorff distance up to isometry; High-dimensional limit; Random metric space; Random walk; Subordinator; Wiener spiral;

D O I：

10.1016/j.spa.2024.104428

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：

A crinkled subordinator is an l(2)-valued random process which can be thought of as a version of the usual one-dimensional subordinator with each out of countably many jumps being in a direction orthogonal to the directions of all other jumps. We show that the path of a d-dimensional random walk with n independent identically distributed steps with heavytailed distribution of the radial components and asymptotically orthogonal angular components converges in distribution in the Hausdorff distance up to isometry and also in the Gromov-Hausdorff sense, if viewed as a random metric space, to the closed range of a crinkled subordinator, as d, n -> infinity.

引用

页数：13

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