The Annals of Probability
- Ann. Probab.
- Volume 45, Number 2 (2017), 1160-1189.
Climbing down Gaussian peaks
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.
Ann. Probab., Volume 45, Number 2 (2017), 1160-1189.
Received: January 2015
Revised: November 2015
First available in Project Euclid: 31 March 2017
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Adler, Robert J.; Samorodnitsky, Gennady. Climbing down Gaussian peaks. Ann. Probab. 45 (2017), no. 2, 1160--1189. doi:10.1214/15-AOP1083. https://projecteuclid.org/euclid.aop/1490947316