ON THE EXISTENCE OF PATHS BETWEEN POINTS IN HIGH LEVEL EXCURSION SETS OF GAUSSIAN RANDOM FIELDS

被引：13

作者：

Adler, Robert J. ^{[1
]}

Moldavskaya, Elina ^{[1
]}

Samorodnitsky, Gennady ^{[2
]}

机构：

[1] Technion Israel Inst Technol, IL-32000 Haifa, Israel

[2] Cornell Univ, ORIE, Ithaca, NY 14853 USA

来源：

ANNALS OF PROBABILITY | 2014年 / 42卷 / 03期

基金：

以色列科学基金会;

关键词：

Gaussian process; excursion set; large deviations; exceedence probabilities; connected component; optimal path; energy of measures;

D O I：

10.1214/12-AOP794

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：

The structure of Gaussian random fields over high levels is a well researched and well understood area, particularly if the field is smooth. However, the question as to whether or not two or more points which lie in an excursion set belong to the same connected component has constantly eluded analysis. We study this problem from the point of view of large deviations, finding the asymptotic probabilities that two such points are connected by a path laying within the excursion set, and so belong to the same component. In addition, we obtain a characterization and descriptions of the most likely paths, given that one exists.

引用

页码：1020 / 1053

页数：34

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