ON THE EXISTENCE OF PATHS BETWEEN POINTS IN HIGH LEVEL EXCURSION SETS OF GAUSSIAN RANDOM FIELDS
成果类型：
Article
署名作者：
Adler, Robert J.; Moldavskaya, Elina; Samorodnitsky, Gennady
署名单位：
Technion Israel Institute of Technology; Cornell University
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/12-AOP794
发表日期：
2014
页码：
1020-1053
关键词：
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.