Modern physics is confronted with a large variety of complex spatial patterns. Although both spatial statisticians and statistical physicists study random geometrical structures, there has been only little interaction between the two up to now because of different traditions and languages.
This volume aims to change this situation by presenting in a clear way fundamental concepts of spatial statistics which are of great potential value for condensed matter physics and materials sciences in general, and for porous media, percolation and Gibbs processes in particular. Geometric aspects, in particular ideas of stochastic and integral geometry, play a central role throughout. With nonspecialist researchers and graduate students also in mind, prominent physicists give an excellent introduction here to modern ideas of statistical physics pertinent to this exciting field of research.
I. Spatial Statistics and Point Processes: Basic Ideas of Spatial Statistics. Stationary Models in Stochastic Geometry. Statistical Analysis of Large-Scale Strucutre in the Universe. Dynamics of Stucture Formation in Thin Film Liquid Films.- II. Integral Geometry and Morphology of Patterns: Mixed Measures and Inhomogeneous Boolean Models. Additivity, Convexity, and Beyond. Considerations About the Estimation of the Size Distribution in Wicksell's Corpuscule Problem. Local Porosity Theory and Stochastic Reconstruction for Porous Media. Stochastic Models as Tools for the Analysis of Decomposition and Crystallisation Phenomena in Solids.- III. Phase Transitions and Simulations of Hard Particles: Phase Transition and Percolation in Gibbsian Particle Models. Fun with Hard Spheres. Finite Packings and Parametric Density. A Primer on Perfect Simulation. Grand Canonical Simulations of Hard-Disk Systems by Simulated Tempering. Dynamics Triangulations for Granular Media Simulations.