The Annals of Probability

On the existence of paths between points in high level excursion sets of Gaussian random fields

Robert J. Adler, Elina Moldavskaya, and Gennady Samorodnitsky

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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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Ann. Probab., Volume 42, Number 3 (2014), 1020-1053.

First available in Project Euclid: 26 March 2014

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Zentralblatt MATH identifier

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

Gaussian process excursion set large deviations exceedence probabilities connected component optimal path energy of measures


Adler, Robert J.; Moldavskaya, Elina; Samorodnitsky, Gennady. On the existence of paths between points in high level excursion sets of Gaussian random fields. Ann. Probab. 42 (2014), no. 3, 1020--1053. doi:10.1214/12-AOP794.

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