6:00 pm Wednesday, March 25, 2015
Back Porch Seminar: Stochastic Geometry by Francois Baccelli (UT) in Schedler and Lawn's Back Porch
Stochastic geometry is a branch of probability theory focusing on random phenomena in the Euclidean space. Kolmogorov is credited for having built the foundations of the field – the Boolean model and the Poisson-Voronoi tessellation – for analyzing the growth of crystals. Nowadays stochastic geometry is widely used in computer science (image analysis), communication sciences (wireless networks, information theory), cosmology (analysis of the organization of galaxies), biology and life sciences. The modern theory is a very active branch of probability theory with a rich interplay with topology (topology of closed sets), algebraic topology (e.g. for the Boolean model), ergodic theory (Palm probabilities), convex analysis (Euler’s characteristics, intrinsic volumes), and computational probability. In the first part of the seminar, I will give a survey of the theory of point processes in the Euclidean space and of three fundamental objects of stochastic geometry built from point processes: the Boolean model, random tessellations and shot-noise fields. In the second part, I will give a survey of the connection between stochastic geometry in high dimension and information theory which I currently investigate with V. Anantharam. Submitted by
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