Random Fields and Geometry

• Main Authors: Adler, Robert J. (Author), Taylor, Jonathan E. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2007.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematics.; Geometry.; Probabilities.; Physics.; Statistics.; Probability Theory and Stochastic Processes.; Statistics, general.; Mathematical Methods in Physics.

This monograph is devoted to a completely new approach to geometric problems arising in the study of random fields. The groundbreaking material in Part III, for which the background is carefully prepared in Parts I and II, is of both theoretical and practical importance, and striking in the way in w...

Table of Contents:

• Gaussian Processes
• Gaussian Fields
• Gaussian Inequalities
• Orthogonal Expansions
• Excursion Probabilities
• Stationary Fields
• Geometry
• Integral Geometry
• Differential Geometry
• Piecewise Smooth Manifolds
• Critical Point Theory
• Volume of Tubes
• The Geometry of Random Fields
• Random Fields on Euclidean Spaces
• Random Fields on Manifolds
• Mean Intrinsic Volumes
• Excursion Probabilities for Smooth Fields
• Non-Gaussian Geometry.