Titlebook: Statistical Physics and Spatial Statistics; The Art of Analyzing Klaus R. Mecke,Dietrich Stoyan Conference proceedings 2000 Springer-Verlag

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Mixed Measures and Inhomogeneous Boolean Modelsalued parameter, the intensity measure. Whereas classically Boolean models were studied which are stationary and isotropic, some of the methods and results have been extended to the non-isotropic situation. More recent investigations consider inhomogeneous Boolean models, i.e. random sets without an

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Additivity, Convexity, and Beyond: Applications of Minkowski Functionals in Statistical Physics morphological descriptors, known as Minkowski functionals, which are related to curvature integrals and do not only characterize connectivity (topology) but also content and shape (geometry) of spatial patterns. Since many physical phenomena depend essentially on the geometry of spatial structures,

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Stochastic Models as Tools for the Analysis of Decomposition and Crystallisation Phenomena in Solidsal nucleation-and-growth model and on methods developed within the framework of stochastic geometry. It is shown that the Boolean model easily reproduces the theory proposed by Kolmogorov, Johnson, Mehl, and Avrami for the kinetics of random second phase formation in solids. Additionally, the mathem

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Phase Transition and Percolation in Gibbsian Particle Modelsrandom-graph models. In particular, we describe a random-geometric approach to the phase transition in the continuum Ising model of two species of particles with soft or hard interspecies repulsion. We comment also on the related area-interaction process and on perfect simulation.

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