CLIMBING DOWN GAUSSIAN PEAKS
成果类型：
Article
署名作者：
Adler, Robert J.; 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：
10.1214/15-AOP1083
发表日期：
2017
页码：
1160-1189
关键词：
摘要：
How likely is the high level of a continuous Gaussian random field on an Euclidean space to have a hole of a certain dimension and depth? Questions of this type are difficult, but in this paper we make progress on questions shedding new light in existence of holes. How likely is the field to be above a high level on one compact set (e.g., a sphere) and to be below a fraction of that level on some other compact set, for example, at the center of the corresponding ball? How likely is the field to be below that fraction of the level anywhere inside the ball? We work on the level of large deviations.
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