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On the existence of paths between points in high level excursion sets of Gaussian random fields. (English) Zbl 1301.60041
Let \(X(t)\), \(t\in\mathbb{R}^d\), be a real-valued sample continuous Gaussian random field. Given a level \(u\), the excursion set of \(X\) above the level \(u\) is the random set \(A_u= \{t\in\mathbb{R}^d: X(t)> u\}\). The authors study the following question: Given that two points in \(\mathbb{R}^d\) belong to the excursion set, what is the probability that they belong to the same path-connected component of the excursion set?

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