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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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