Geometry of Level Sets of Random Fields, Kac–Rice Formulas, Hermite Expansions and Applications

Diego Armentano is a professor at the Instituto de Estadística (Universidad de la República, Uruguay). His research lies at the intersection of probability theory and numerical analysis, with a particular focus on random algebraic geometry and the complexity of numerical algorithms.Jean-Marc Azaïs is an emeritus professor at the Institut de Mathématiques de Toulouse, Université de Toulouse, France. He has worked on various topics including statistics, probability and geometry of random fields. He has also authored many articles and directed many PhDs. In 2009, he authored a monograph on geometry of random fields with Mario Wschebor.Federico Dalmao is a professor at the Departamento de Matemática y Estadística, Universidad de la República, Salto, Uruguay. The focus of his research is on the geometric properties of stochastic processes and random fields.Yohann De Castro, a professor at Institut Camille Jordan, École Centrale Lyon, specializes in the intersection of statistics, probability, and optimization. His research focuses on stochastic and high-dimensional geometry, convex and stochastic optimization, and latent position models.Céline Delmas is a researcher at the French National Research Institute for Agriculture, Food and Environment (INRAE) in the Applied Mathematics and Informatics Unit. She is a statistician whose research focuses on Gaussian fields, statistical inference and modeling.José Rafael León Ramos is a mathematician specializing in probability theory and mathematical statistics. He is a professor at the Universidad de la República (Uruguay) and was a former full professor at the Universidad Central de Venezuela. His research focuses on stochastic processes, Gaussian fields, and statistical inference. He has published extensively and is the co-author of several monographs, including volumes in the Springer series, Lecture Notes in Statistics.Ernesto Mordecki is a professor at the Centro de Matemática, Universidad de la República, Montevideo. He earned his PhD at the Steklov Mathematical Institute (Moscow, 1994) under Albert Shiryaev, specializing in optimal stopping, Lévy processes, and mathematical finance. In addition, in 2015, he was elected to the Academy of Sciences of Uruguay.

• Chapter 1. The Kac–Rice Formula, Dimension 1.- Chapter 2. Multidimensional Methods.- Chapter 3. Distributions, Expectations and Moments for Gaussian Processes and Fields.- Chapter 4. Hermite Expansions of Level Functionals.- Chapter 5. Critical Points of Isotropic Gaussian Fields.- Chapter 6. Second Maximum and Sparse Models.- Chapter 7. Shot Noise Processes.- Chapter 8. Related Works.