Iteration Stable Tessellations: Random Tessellations Generated by Division of Polytopes

This book provides a comprehensive introduction to STIT tessellations, a class of random tessellations characterized by their stability under the iteration of tessellations. Emerging from a stochastic process of successive subdivisions of polytopes in Euclidean space, this model lends itself to a rigorous theoretical analysis. Beyond their theoretical significance, STIT tessellations serve as valuable reference models for real-world applications — ranging from crack formation in materials science and fragmentation processes in geology to the subdivision of high-dimensional data sets in machine learning and the analysis of spatial patterns in communication systems. Divided into four parts, this volume systematically explores the construction and analysis of tessellation-valued stochastic processes, emphasizing the interplay between geometric concepts and probabilistic methods. It positions STIT tessellations alongside classical models such as Poisson hyperplane and Poisson–Voronoi tessellations. With its rigorous yet accessible approach, this book is an indispensable resource for researchers and practitioners in stochastic geometry, spatial modelling, and applied mathematics.