On the existence of paths between points in high level excursion sets of Gaussian random fields
Adler, Robert; Moldavskaya, Elina; Samorodnitsky, Gennady
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.
Research supported in part by US-Israel Binational Science Foundation, 2008262, by ARO grant W911NF-07-1-0078, NSF grant DMS-1005903 and NSA grant H98230-11-1-0154 at Cornell University, by Israel Science Foundation, 853/10, by AFOSR FA8655-11-1-3039, by Office for Absorption of New Scientists and ERC grant RCMT152.
Gaussian process; excursion set; large deviations; exceedance probabilities; connected component; optimal path; energy of measures