Name: Geometry of Level Sets of Random Fields, Kac–Rice Formulas, Hermite Expansions and Appl
Price: 156 CHF
Availability: InStock
ISBN: 978-3-032-29143-1

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Springer

The book "Geometry of Level Sets of Random Fields, Kac–Rice Formulas, Hermite Expansions and Applications" offers a comprehensive introduction to the modern theory of the geometric properties of random fields and their interdisciplinary applications. The first five chapters focus on the theoretical and mathematical foundations of the expected mass numbers of level sets, including critical points and Morse theory. A simplified proof of the Kac-Rice formula is presented, adapted to non-Gaussian cases, and the issue of the finiteness of moments is addressed. The text combines pedagogical explanations with current, powerful mathematical results. In particular, Chapter 4 provides an accessible presentation of the Hermite representation, the diagram formula, and the fourth moment theorem to establish central limit theorems for the mass of the level set without resorting to complex tools like Malliavin calculus. The later chapters demonstrate the practical application of these tools in areas such as high-dimensional statistics, theoretical physics, optics, and the study of critical points, concluding with a comprehensive bibliographic overview. This monograph will be useful for students and researchers in probability theory, geometry, and applied sciences, offering powerful geometric tools and explicit examples for solving modern problems involving random fields.

Actual product image Geometry of Level Sets of Random Fields, Kac–Rice Formulas, Hermite Expansions and Appl (English, Hardcover, Céline Delmas, Diego Armentano, Ernesto Mordecki, Federico Dalmao, Jean-Marc Azaïs, José Rafael León, Yohann De Castro)

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