Name: Geometry of Level Sets of Random Fields, Kac–Rice Formulas, Hermite Expansions and Applications (en Inglés)
SKU: 67248289
Price: 440857.00 COP
Availability: InStock
Author: Diego Armentano
ISBN: 9783032291431

portada Geometry of Level Sets of Random Fields, Kac–Rice Formulas, Hermite Expansions and Applications (en Inglés)

Geometry of Level Sets of Random Fields, Kac–Rice Formulas, Hermite Expansions and Applications (en Inglés)

Formato

Libro Físico

Editorial

Springer Nature Switzerland

Autor

Diego Armentano

Año

2026

Idioma

Inglés

Encuadernación

Tapa Dura

Dimensiones

23.5x15.5 cm

ISBN13

9783032291431

Geometry of Level Sets of Random Fields, Kac–Rice Formulas, Hermite Expansions and Applications (en Inglés)

Diego Armentano (Autor) · Springer Nature Switzerland · Tapa Dura

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Reseña del libro "Geometry of Level Sets of Random Fields, Kac–Rice Formulas, Hermite Expansions and Applications (en Inglés)"

This book presents the modern theory of the geometrical characteristics of random fields and explores their interdisciplinary applications. The first five chapters concentrate on the theoretical and mathematical foundations of the expected measure of level sets, including critical points and Morse theory. They provide a streamlined proof of the Kac-Rice formula, adapted to non-Gaussian cases, and address the problem of the finiteness of moments.

The text balances pedagogical explanations with recent, powerful mathematical results. Chapter 4 notably offers an accessible presentation of Hermite representation, the diagram formula, and the fourth moment theorem to establish central limit theorems for the measure of the level set, intentionally avoiding overly complex tools like Malliavin calculus. The latter chapters demonstrate the practical application of these tools across domains such as high-dimensional statistics, theoretical physics, optics and the study of critical points, concluding with a comprehensive bibliographic review.

This monograph will be useful for students and researchers in probability theory, geometry, and applied sciences. It will equip them with powerful geometric tools and explicit examples to solve modern problems involving random fields.