Iteration Stable Tessellations
Description
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.
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Persons
Werner Nagel , born 1952, pursued his studies in mathematics in Jena, where he earned his diploma in 1974. He obtained his PhD in 1979 at the Mining Academy Freiberg and completed his habilitation in mathematics in 1992 at the University of Jena. From 1992 until 2018, he served as an Assistant Professor at the University of Jena. His main research focus is on Stochastic Geometry, in particular random tessellations.
Christoph Thäle , born 1984, pursued his studies in mathematics at the University of Jena, earning his diploma in 2007. He obtained his PhD in 2010 from the Université de Fribourg in Switzerland. Following his doctoral studies, he held postdoctoral positions in Osnabrück and Bochum from 2010 to 2013. Between 2013 and 2016, he served as an Assistant Professor, and since 2016 he has been a Full Professor in Probability at Ruhr University Bochum. His main research focus is spatial random structures.
Viola Weiß, born 1959, pursued her studies in mathematics in Jena, where she earned her diploma in 1982. She obtained her PhD in 1988 at the University of Jena. From 1988 until 1999, she held postdoctoral positions at the University of Jena. Since 1999 she has been a Full Professor in Mathematics at the University of Applied Sciences of Jena. Her research focus is on Stochastic Geometry, in particular random tessellations.