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March 2017 Climbing down Gaussian peaks
Robert J. Adler, Gennady Samorodnitsky
Ann. Probab. 45(2): 1160-1189 (March 2017). DOI: 10.1214/15-AOP1083


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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Robert J. Adler. Gennady Samorodnitsky. "Climbing down Gaussian peaks." Ann. Probab. 45 (2) 1160 - 1189, March 2017.


Received: 1 January 2015; Revised: 1 November 2015; Published: March 2017
First available in Project Euclid: 31 March 2017

zbMATH: 06797088
MathSciNet: MR3630295
Digital Object Identifier: 10.1214/15-AOP1083

Primary: 60F10, 60G15
Secondary: 60G17, 60G60, 60G70

Rights: Copyright © 2017 Institute of Mathematical Statistics


Vol.45 • No. 2 • March 2017
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