RELATIVE COMPLEXITY OF RANDOM WALKS IN RANDOM SCENERY IN THE ABSENCE OF A WEAK INVARIANCE PRINCIPLE FOR THE LOCAL TIMES

被引：1

作者：

Deligiannidis, George ^{[1
]}

Kosloff, Zemer ^{[2
]}

机构：

[1] Univ Oxford, Dept Stat, 24-29 St Giles, Oxford OX1 3LB, England

[2] Univ Warwick, Math Inst, Zeeman Bldg, Coventry CV4 7AL, W Midlands, England

来源：

ANNALS OF PROBABILITY | 2017年 / 45卷 / 04期

关键词：

Random walk in random scenery; relative complexity; entropy; Folner sequence; MEASURE-PRESERVING TRANSFORMATIONS; 2-DIMENSIONAL RANDOM-WALKS; LOOSELY BERNOULLI; LIMIT-THEOREM; ENTROPY; GENERATORS;

D O I：

10.1214/16-AOP1118

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：

We answer a question of Aaronson about the relative complexity of Random Walks in Random Sceneries driven by either aperiodic two-dimensional random walks, two-dimensional Simple Random walk, or by aperiodic random walks in the domain of attraction of the Cauchy distribution. A key step is proving that the range of the random walk satisfies the Folner property almost surely.

引用

页码：2505 / 2532

页数：28

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