Statistical Physics and Spatial Statistics: The Art of Analyzing and Modeling Spatial Structures and Pattern Formation

Dietrich Stoyan (auth.), Klaus R. Mecke, Dietrich Stoyan (eds.)354067750X, 9783540677505

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.

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Table of contents :
Basic Ideas ofSpatial Statistics….Pages 3-21
Stationary Models in Stochastic Geometry – Palm Distributions as Distributions of Typical Elements. An Approach Without Limits….Pages 22-35
Statistical Analysis of Large-Scale Structure in the Universe….Pages 36-71
Dynamics ofStructure Formation in Thin Liquid Films: A Special Spatial Analysis….Pages 72-91
Mixed Measures and Inhomogeneous Boolean Models….Pages 95-110
Additivity, Convexity, and Beyond: Applications of Minkowski Functionals in Statistical Physics….Pages 111-184
Considerations About the Estimation ofthe Size Distribution in Wicksell’s Corpuscle Problem….Pages 185-202
Local Porosity Theory and Stochastic Reconstruction for Porous Media….Pages 203-241
Stochastic Models as Tools for the Analysis of Decomposition and Crystallisation Phenomena in Solids….Pages 242-264
Phase Transition and Percolation in Gibbsian Particle Models….Pages 267-294
Fun with Hard Spheres….Pages 295-331
Finite Packings and Parametric Density….Pages 332-348
A Primer on Perfect Simulation….Pages 349-378
Grand Canonical Simulations ofHard-Disk Systems by Simulated Tempering….Pages 379-393
Dynamic Triangulations for Granular Media Simulations….Pages 394-409