منابع مشابه
Random Conical Tessellations
We consider tessellations of the Euclidean (d− 1)-sphere by (d− 2)-dimensional great subspheres or, equivalently, tessellations of Euclidean d-space by hyperplanes through the origin; these we call conical tessellations. For random polyhedral cones defined as typical cones in a conical tessellation by random hyperplanes, and for their dual cones, we study expectations of certain geometric funct...
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Generalizations of various random tessellation models generated by Poisson point processes are proposed and their functional probability P (K) is given. They are interpreted as characteristics of Boolean random functions models, which provide a generic way of simulation of general random tessellations.
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We consider random tessellations T in R2 and Coxian point processes whose driving measure is concentrated on the edges of T . In particular, we discuss several classes of Poisson-type tessellations which can describe e.g. the infrastructure of telecommunication networks, whereas the Cox processes on their edges can describe the locations of network components. An important quantity associated w...
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Random tessellations form a very important field in stochastic geometry. They pose many interesting mathematical problems and have numerous important applications in many branches of natural sciences and engineering, as this volume shows. This contribution aims to present mathematical basic facts as well as statistical ideas for random tessellations of the d-dimensional Euclidean space R. Havin...
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Given a subset K of the unit Euclidean sphere, we estimate the minimal number m = m(K) of hyperplanes that generate a uniform tessellation of K, in the sense that the fraction of the hyperplanes separating any pair x, y ∈ K is nearly proportional to the Euclidean distance between x and y. Random hyperplanes prove to be almost ideal for this problem; they achieve the almost optimal bound m = O(w...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2016
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-016-9788-0