Random Fields and Geometry

Preface.- Part I. Gaussian Processes. Gaussian Fields. Gaussian Inequalities. Orthogonal Expansions. Excursion Probabilities. Stationary Fields.- Parat II. Geometry. Integral Geometry. Differential Geometry. Piecewise Smooth Manifolds. Critical Point Theory. Volume of Tubes.- Part III. 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.- References.- Index.