Climbing down Gaussian peaks

Citation
J. Adler, Robert et Samorodnitsky, Gennady, Climbing down Gaussian peaks, Annals of probability , 45(2), 2017, pp. 1160-1189
Journal title
ISSN journal
00911798
Volume
45
Issue
2
Year of publication
2017
Pages
1160 - 1189
Database
ACNP
SICI code
Abstract
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.