Rolf Schneider Book order

Exploring the intersection of probability theory and geometry, this book delves into random mosaics created by Poisson processes of hyperplanes. It examines the independence properties of these processes and their long-range effects, revealing a multitude of phenomena significant in both geometric and probabilistic contexts. The text covers various perspectives and comprehensively discusses established literature, making it a valuable resource for graduate students, professional mathematicians, and researchers across multiple disciplines, including physics and engineering.

Focusing on geometric applications, the book introduces convex cones and explores their fundamental properties. It covers key geometric functionals like conic intrinsic volumes and Grassmann angles, while also developing general versions of important formulas such as the Steiner and kinematic formulas. Selected examples from diverse topics, including polytope theory, stochastic geometry, and Brunn-Minkowski theory, illustrate the concepts, making it a comprehensive resource for understanding the geometry of convex cones.

Stochastic geometry deals with models for random geometric structures. Its early beginnings are found in playful geometric probability questions, and it has vigorously developed during recent decades, when an increasing number of real-world applications in various sciences required solid mathematical foundations. Integral geometry studies geometric mean values with respect to invariant measures and is, therefore, the appropriate tool for the investigation of random geometric structures that exhibit invariance under translations or motions. Stochastic and Integral Geometry provides the mathematically oriented reader with a rigorous and detailed introduction to the basic stationary models used in stochastic geometry – random sets, point processes, random mosaics – and to the integral geometry that is needed for their investigation. The interplay between both disciplines is demonstrated by various fundamental results. A chapter on selected problems about geometric probabilities and an outlook to non-stationary models are included, and much additional information is given in the section notes.