Stochastic Geometry: Selected Topics

Viktor Benes, Jan Rataj1402081022, 9781402081033, 9781402081026

Stochastic geometry, based on current developments in geometry, probability and measure theory, makes possible modeling of two- and three-dimensional random objects with interactions as they appear in the microstructure of materials, biological tissues, macroscopically in soil, geological sediments etc. In combination with spatial statistics it is used for the solution of practical problems such as the description of spatial arrangements and the estimation of object characteristics. A related field is stereology, which makes possible inference on the structures, based on lower-dimensional observations. Unfolding problems for particle systems and extremes of particle characteristics are studied. The reader can learn about current developments in stochastic geometry with mathematical rigor on one hand and find applications to real microstructure analysis in natural and material sciences on the other hand. Audience: This volume is suitable for scientists in mathematics, statistics, natural sciences, physics, engineering (materials), microscopy and image analysis, as well as postgraduate students in probability and statistics.