High Level Excursion Set Geometry for Non-gaussian Infinitely Divisible Random Fields
نویسندگان
چکیده
over high levels u. For a large class of such random fields we compute the u → ∞ asymptotic joint distribution of the numbers of critical points, of various types, of X in Au, conditional on Au being non-empty. This allows us, for example, to obtain the asymptotic conditional distribution of the Euler characteristic of the excursion set. In a significant departure from the Gaussian situation, the high level excursion sets for these random fields can have quite a complicated geometry. Whereas in the Gaussian case non-empty excursion sets are, with high probability, roughly ellipsoidal, in the more general infinitely divisible setting almost any shape is possible.
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