The Annals of Probability

Climbing down Gaussian peaks

Robert J. Adler and Gennady Samorodnitsky

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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.

Article information

Source
Ann. Probab., Volume 45, Number 2 (2017), 1160-1189.

Dates
Received: January 2015
Revised: November 2015
First available in Project Euclid: 31 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.aop/1490947316

Digital Object Identifier
doi:10.1214/15-AOP1083

Mathematical Reviews number (MathSciNet)
MR3630295

Zentralblatt MATH identifier
06797088

Subjects
Primary: 60G15: Gaussian processes 60F10: Large deviations
Secondary: 60G60: Random fields 60G70: Extreme value theory; extremal processes 60G17: Sample path properties

Keywords
Gaussian process excursion set large deviations exceedence probabilities topology

Citation

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


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References

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