Książki

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 which problems arising in geometry and probability are beautifully intertwined.

"Random Fields and Geometry" will be useful for probabilists and statisticians, and for theoretical and applied mathematicians who wish to learn about new relationships between geometry and probability. It will be helpful for graduate students in a classroom setting, or for self-study. Finally, this text will serve as a basic reference for all those interested in the companion volume of the applications of the theory.

 

Random Fields and Geometry

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.