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Pré-Publication, Document De Travail Année : 2022

Kac-Rice Formula: A contemporary overview of the main results and applications

Formule de Kac-Rice : un aperçu contemporain des principaux résultats et applications

Résumé

The book develops the fundamental ideas of the famous Kac-Rice formula for vectorvalued random fields. This formula allows to compute the expectation and moments of the measure, and integrals with respect to this measure, of the sets of levels of such fields. After a presentation of the historical context of the Kac-Rice formula, we give an elementary demonstration of the co-area formula. This formula replaces the change of variable formula in multiple integrals and a direct application of this formula gives the Kac-Rice formula for almost all levels. We emphasize the necessity of having the formula for all levels, because for some applications one needs, for example, the formula for level zero.
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Dates et versions

hal-03665428 , version 1 (13-05-2022)

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Corinne Berzin, Alain Latour, José León. Kac-Rice Formula: A contemporary overview of the main results and applications. 2022. ⟨hal-03665428⟩
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