Stochastic Geometry: Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 13-18, 2004 (Lecture Notes in Mathematics / Fondazione C.I.M.E., Firenze)

Stochastic Geometry is the mathematical discipline which studies mathematical models for random geometric structures, as they appear frequently in almost all natural sciences or technical fields. Although its roots can be traced back to the 18th century (the Buffon needle problem), the modern theory of random sets was founded by D. Kendall and G. Matheron in the early 1970's. Its rapid development was influenced by applications in Spatial Statistics and by its close connections to Integral Geometry. The volume __"Stochastic Geometry"__ contains the lectures given at the CIME summer school in Martina Franca in September 1974. The four main lecturers covered the areas of Spatial Statistics, Random Points, Integral Geometry and Random Sets, they are complemented by two additional contributions on Random Mosaics and Crystallization Processes. The book presents an up-to-date description of important parts of Stochastic Geometry. Stochastic Geometry is the mathematical discipline which studies mathematical models for random geometric structures, as they appear frequently in almost all natural sciences or technical fields. Although its roots can be traced back to the 18th century (the Buffon needle problem), the modern theory of random sets was founded by D. Kendall and G. Matheron in the early 1970's. Its rapid development was influenced by applications in Spatial Statistics and by its close connections to Integral Geometry. The volume "Stochastic Geometry" contains the lectures given at the CIME summer school in Martina Franca in September 2004. The four main lecturers covered the areas of Spatial Statistics, Random Points, Integral Geometry and Random Sets, they are complemented by two additional contributions on Random Mosaics and Crystallization Processes. The book presents an up-to-date description of important parts of Stochastic Geometry. Spatial Point Processes And Their Applications / Adrian Baddeley -- Random Polytopes, Convex Bodies, And Approximation / Imre Bárány -- Integral Geometric Tools For Stochastic Geometry / Rolf Schneider -- Random Sets (in Particular Boolean Models) / Wolfgang Weil -- Random Mosaics / Daniel Hug -- On The Evolution Equations Of Mean Geometric Densities For A Class Of Space And Time Inhomogeneous Stochastic Birth-and-growth Processes / Vincenzo Capasso, Elena Villa. A. Baddeley ... [et Al.] ; With Additional Contributions By D. Hug, V. Capasso, E. Villa ; Editor: W. Weil. Includes Bibliographical References And Index. Front Matter....Pages I-XII Spatial Point Processes and their Applications....Pages 1-75 Random Polytopes, Convex Bodies, and Approximation....Pages 77-118 Integral Geometric Tools for Stochastic Geometry....Pages 119-184 Random Sets (in Particular Boolean Models)....Pages 185-245 Random Mosaics....Pages 247-266 On the Evolution Equations of Mean Geometric Densities for a Class of Space and Time Inhomogeneous Stochastic Birth-and-growth Processes....Pages 267-281 Back Matter....Pages 283-292