Daniel Hug Knihy

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 convex geometry in Euclidean space, this book introduces fundamental concepts and results, progressing to the Brunn-Minkowski theory, including mixed volumes and the Brunn-Minkowski inequality. It also explores key topics like surface area measures, projection functions, zonoids, and geometric valuations. An introduction to integral-geometric formulas concludes the text. The inclusion of numerous exercises and supplementary materials enhances the learning experience, making it a comprehensive resource for students and researchers alike.