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Title: On the existence of paths between points in high level excursion sets of Gaussian random fields
Authors: Adler, Robert
Moldavskaya, Elina
Samorodnitsky, Gennady
Keywords: Gaussian process
excursion set
large deviations
exceedance probabilities
connected component
optimal path
energy of measures
Issue Date: 27-Mar-2012
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.
Appears in Collections:ORIE Technical Reports

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