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May 2014 On the existence of paths between points in high level excursion sets of Gaussian random fields
Robert J. Adler, Elina Moldavskaya, Gennady Samorodnitsky
Ann. Probab. 42(3): 1020-1053 (May 2014). DOI: 10.1214/12-AOP794

Abstract

The structure of Gaussian random fields over high levels is a well researched and well understood area, particularly if the field is smooth. However, the question as to whether or not two or more points which lie in an excursion set belong to the same connected component has constantly eluded analysis. We study this problem from the point of view of large deviations, finding the asymptotic probabilities that two such points are connected by a path laying within the excursion set, and so belong to the same component. In addition, we obtain a characterization and descriptions of the most likely paths, given that one exists.

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Robert J. Adler. Elina Moldavskaya. Gennady Samorodnitsky. "On the existence of paths between points in high level excursion sets of Gaussian random fields." Ann. Probab. 42 (3) 1020 - 1053, May 2014. https://doi.org/10.1214/12-AOP794

Information

Published: May 2014
First available in Project Euclid: 26 March 2014

zbMATH: 1301.60041
MathSciNet: MR3189065
Digital Object Identifier: 10.1214/12-AOP794

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

Rights: Copyright © 2014 Institute of Mathematical Statistics

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Vol.42 • No. 3 • May 2014
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