Threshold Phenomena For Random Cones
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Threshold Phenomena For Random Cones
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Author : Daniel Hug
language : en
Publisher:
Release Date : 2022
Threshold Phenomena For Random Cones written by Daniel Hug and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with categories.
Abstract: We consider an even probability distribution on the d-dimensional Euclidean space with the property that it assigns measure zero to any hyperplane through the origin. Given N independent random vectors with this distribution, under the condition that they do not positively span the whole space, the positive hull of these vectors is a random polyhedral cone (and its intersection with the unit sphere is a random spherical polytope). It was first studied by Cover and Efron. We consider the expected face numbers of these random cones and describe a threshold phenomenon when the dimension d and the number N of random vectors tend to infinity. In a similar way we treat the solid angle, and more generally the Grassmann angles. We further consider the expected numbers of k-faces and of Grassmann angles of index d−k when also k tends to infinity
Convex Cones
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Author : Rolf Schneider
language : en
Publisher: Springer Nature
Release Date : 2022-09-21
Convex Cones written by Rolf Schneider and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-21 with Mathematics categories.
This book provides the foundations for geometric applications of convex cones and presents selected examples from a wide range of topics, including polytope theory, stochastic geometry, and Brunn–Minkowski theory. Giving an introduction to convex cones, it describes their most important geometric functionals, such as conic intrinsic volumes and Grassmann angles, and develops general versions of the relevant formulas, namely the Steiner formula and kinematic formula. In recent years questions related to convex cones have arisen in applied mathematics, involving, for example, properties of random cones and their non-trivial intersections. The prerequisites for this work, such as integral geometric formulas and results on conic intrinsic volumes, were previously scattered throughout the literature, but no coherent presentation was available. The present book closes this gap. It includes several pearls from the theory of convex cones, which should be better known.
Threshold Phenomena Ans Influence With Some Perspective From Mathematics Computer Science And Economics
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Author : Gil Kalai
language : en
Publisher:
Release Date : 2005
Threshold Phenomena Ans Influence With Some Perspective From Mathematics Computer Science And Economics written by Gil Kalai and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.
First Passage Phenomena And Their Applications
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Author : Ralf Metzler
language : en
Publisher: World Scientific
Release Date : 2014-03-21
First Passage Phenomena And Their Applications written by Ralf Metzler and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-21 with Science categories.
The book contains review articles on recent advances in first-passage phenomena and applications contributed by leading international experts. It is intended for graduate students and researchers who are interested in learning about this intriguing and important topic.
Diverse Quantization Phenomena In Layered Materials
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Author : Chiun-Yan Lin
language : en
Publisher: CRC Press
Release Date : 2019-12-06
Diverse Quantization Phenomena In Layered Materials written by Chiun-Yan Lin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-06 with Science categories.
This monograph offers a comprehensive overview of diverse quantization phenomena in layered materials, covering current mainstream experimental and theoretical research studies, and presenting essential properties of layered materials along with a wealth of figures. This book illustrates commonly used synthesis methods of these 2D materials and compares the calculated results and experimental measurements, including novel features not yet reported. The book also discusses experimental measurements of magnetic quantization, theoretical modeling for studying systems and covers diversified magneto-electronic properties, magneto-optical selection rules, unusual quantum Hall conductivities, and single- and many-particle magneto-Coulomb excitations. Rich and unique behaviors are clearly revealed in few-layer graphene systems with distinct stacking configuration, stacking-modulated structures, silicon-doped lattices, bilayer silicene/germanene systems with the bottom-top and bottom-bottom buckling structures, monolayer and bilayer phosphorene systems, and quantum topological insulators. The generalized tight-binding model, the static and dynamic Kubo formulas, and the random-phase approximation are developed/modified to thoroughly explore the fundamental properties and propose the concise physical pictures. Different high-resolution experimental measurements are discussed in detail, and they are consistent with the theoretical predictions. Aimed at readers working in materials science, physics, and engineering this book should be useful for potential applications in energy storage, electronic devices, and optoelectronic devices.
High Dimensional Probability
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Author : Roman Vershynin
language : en
Publisher: Cambridge University Press
Release Date : 2018-09-27
High Dimensional Probability written by Roman Vershynin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-27 with Business & Economics categories.
An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Scientific And Technical Aerospace Reports
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Author :
language : en
Publisher:
Release Date : 1992
Scientific And Technical Aerospace Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Aeronautics categories.
Foundations Of Data Science
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Author : Avrim Blum
language : en
Publisher: Cambridge University Press
Release Date : 2020-01-23
Foundations Of Data Science written by Avrim Blum and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-23 with Computers categories.
Covers mathematical and algorithmic foundations of data science: machine learning, high-dimensional geometry, and analysis of large networks.
Stochastic And Integral Geometry
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Author : R.V. Ambartzumian
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Stochastic And Integral Geometry written by R.V. Ambartzumian and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Journal Of The Optical Society Of America
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Author :
language : en
Publisher:
Release Date : 1978
Journal Of The Optical Society Of America written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Optical instruments categories.