Geometry and Physics of Spatial Random Systems

This book introduces the geometry and physics of complex, disordered materials such as foams, granular assemblies, paper, catalysts, and amorphous solids. It explains how modern stochastic and integral geometry can be used to describe spatial structure and to understand how morphology influences physical properties.Key topics include the major stochastic models for random media: hard-core particle processes, random tessellations, Boolean models, random fields, and continuum percolation. These mathematical frameworks are consistently linked to physical systems ranging from structured fluids and cellular materials to transport in disordered environments. Integral geometric tools, in particular Minkowski tensors, provide a unifying approach that captures structural information beyond standard correlation measures. The book is designed for learning and self-study. It includes illustrative examples and practical guidance for applying geometric methods in image analysis and spatial statistics. Chapters are organized to help readers gradually build both intuition and a rigorous mathematical understanding. This volume is intended for graduate students and researchers in theoretical physics, mathematics, materials science, and related fields. A basic background in geometry, probability, and continuum physics is helpful, but no prior knowledge of stochastic geometry is required.