Asymptotic Geometric Analysis
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Asymptotic Geometric Analysis Part I
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Author : Shiri Artstein-Avidan
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-06-18
Asymptotic Geometric Analysis Part I written by Shiri Artstein-Avidan and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-18 with Mathematics categories.
The authors present the theory of asymptotic geometric analysis, a field which lies on the border between geometry and functional analysis. In this field, isometric problems that are typical for geometry in low dimensions are substituted by an "isomorphic" point of view, and an asymptotic approach (as dimension tends to infinity) is introduced. Geometry and analysis meet here in a non-trivial way. Basic examples of geometric inequalities in isomorphic form which are encountered in the book are the "isomorphic isoperimetric inequalities" which led to the discovery of the "concentration phenomenon", one of the most powerful tools of the theory, responsible for many counterintuitive results. A central theme in this book is the interaction of randomness and pattern. At first glance, life in high dimension seems to mean the existence of multiple "possibilities", so one may expect an increase in the diversity and complexity as dimension increases. However, the concentration of measure and effects caused by convexity show that this diversity is compensated and order and patterns are created for arbitrary convex bodies in the mixture caused by high dimensionality. The book is intended for graduate students and researchers who want to learn about this exciting subject. Among the topics covered in the book are convexity, concentration phenomena, covering numbers, Dvoretzky-type theorems, volume distribution in convex bodies, and more.
Asymptotic Geometric Analysis
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Author : Monika Ludwig
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-27
Asymptotic Geometric Analysis written by Monika Ludwig 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 2013-03-27 with Mathematics categories.
Asymptotic Geometric Analysis is concerned with the geometric and linear properties of finite dimensional objects, normed spaces, and convex bodies, especially with the asymptotics of their various quantitative parameters as the dimension tends to infinity. The deep geometric, probabilistic, and combinatorial methods developed here are used outside the field in many areas of mathematics and mathematical sciences. The Fields Institute Thematic Program in the Fall of 2010 continued an established tradition of previous large-scale programs devoted to the same general research direction. The main directions of the program included: * Asymptotic theory of convexity and normed spaces * Concentration of measure and isoperimetric inequalities, optimal transportation approach * Applications of the concept of concentration * Connections with transformation groups and Ramsey theory * Geometrization of probability * Random matrices * Connection with asymptotic combinatorics and complexity theory These directions are represented in this volume and reflect the present state of this important area of research. It will be of benefit to researchers working in a wide range of mathematical sciences—in particular functional analysis, combinatorics, convex geometry, dynamical systems, operator algebras, and computer science.
Asymptotic Geometric Analysis
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Author :
language : en
Publisher:
Release Date : 2015
Asymptotic Geometric Analysis written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
Alice And Bob Meet Banach
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Author : Guillaume Aubrun
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-08-30
Alice And Bob Meet Banach written by Guillaume Aubrun and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-30 with Mathematics categories.
The quest to build a quantum computer is arguably one of the major scientific and technological challenges of the twenty-first century, and quantum information theory (QIT) provides the mathematical framework for that quest. Over the last dozen or so years, it has become clear that quantum information theory is closely linked to geometric functional analysis (Banach space theory, operator spaces, high-dimensional probability), a field also known as asymptotic geometric analysis (AGA). In a nutshell, asymptotic geometric analysis investigates quantitative properties of convex sets, or other geometric structures, and their approximate symmetries as the dimension becomes large. This makes it especially relevant to quantum theory, where systems consisting of just a few particles naturally lead to models whose dimension is in the thousands, or even in the billions. Alice and Bob Meet Banach is aimed at multiple audiences connected through their interest in the interface of QIT and AGA: at quantum information researchers who want to learn AGA or apply its tools; at mathematicians interested in learning QIT, or at least the part of QIT that is relevant to functional analysis/convex geometry/random matrix theory and related areas; and at beginning researchers in either field. Moreover, this user-friendly book contains numerous tables and explicit estimates, with reasonable constants when possible, which make it a useful reference even for established mathematicians generally familiar with the subject.
Asymptotic Geometric Analysis
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Author : Shiri Artstein-Avidan
language : en
Publisher:
Release Date : 2024
Asymptotic Geometric Analysis written by Shiri Artstein-Avidan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024 with Functional analysis categories.
Alice And Bob Meet Banach
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Author : Guillaume Aubrun
language : en
Publisher: American Mathematical Society
Release Date : 2024-07-29
Alice And Bob Meet Banach written by Guillaume Aubrun and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-29 with Mathematics categories.
The quest to build a quantum computer is arguably one of the major scientific and technological challenges of the twenty-first century, and quantum information theory (QIT) provides the mathematical framework for that quest. Over the last dozen or so years, it has become clear that quantum information theory is closely linked to geometric functional analysis (Banach space theory, operator spaces, high-dimensional probability), a field also known as asymptotic geometric analysis (AGA). In a nutshell, asymptotic geometric analysis investigates quantitative properties of convex sets, or other geometric structures, and their approximate symmetries as the dimension becomes large. This makes it especially relevant to quantum theory, where systems consisting of just a few particles naturally lead to models whose dimension is in the thousands, or even in the billions. Alice and Bob Meet Banach is aimed at multiple audiences connected through their interest in the interface of QIT and AGA: at quantum information researchers who want to learn AGA or apply its tools; at mathematicians interested in learning QIT, or at least the part of QIT that is relevant to functional analysis/convex geometry/random matrix theory and related areas; and at beginning researchers in either field. Moreover, this user-friendly book contains numerous tables and explicit estimates, with reasonable constants when possible, which make it a useful reference even for established mathematicians generally familiar with the subject.
Cma Amsi Research Symposium Asymptotic Geometric Analysis Harmonic Analysis And Related Topics
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Author : Australian National University. Centre for Mathematics and Its Applications
language : en
Publisher:
Release Date : 2007
Cma Amsi Research Symposium Asymptotic Geometric Analysis Harmonic Analysis And Related Topics written by Australian National University. Centre for Mathematics and Its Applications and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Differential geometry categories.
This volume contains the proceedings of the CMA/AMSI Research Symposium on "Asymptotic Geometric Analysis, Harmonic Analysis and Related Topics'', organized by Andrew Hassell, Alan McIntosh, Shahar Mendelson, Pierre Portal, and Fyodor Sukochev at Murramarang (NSW) in February 2006. The meeting was sponsored by the Centre for Mathematics and its Applications (Australian National University) and the Australian Mathematical Sciences Institute whose support is gratefully acknowledged. The Symposium covered a variety of topics in functional, geometric, and harmonic analysis, and brought together experts, early career researchers, and doctoral students from Australia, Canada, Finland, France, Germany, Israel, and the USA.
Asymptotic Analysis Of Random Walks
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Author : Aleksandr Alekseevich Borovkov
language : en
Publisher: Cambridge University Press
Release Date : 2008
Asymptotic Analysis Of Random Walks written by Aleksandr Alekseevich Borovkov 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 2008 with Asymptotic expansions categories.
This monograph is devoted to studying the asymptotic behaviour of the probabilities of large deviations of the trajectories of random walks, with 'heavy-tailed' (in particular, regularly varying, sub- and semiexponential) jump distributions. It presents a unified and systematic exposition.
On Some Geometric And Functional Inequalities In Asymptotic Geometric Analysis
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Author : Michael A. Roysdon
language : en
Publisher:
Release Date : 2020
On Some Geometric And Functional Inequalities In Asymptotic Geometric Analysis written by Michael A. Roysdon and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with categories.
This dissertation concerns geometric and functional inequalities arising in the areas of convex geometry, asymptotic geometric analysis, and measure theory.
Topological Crystallography
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Author : Toshikazu Sunada
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-23
Topological Crystallography written by Toshikazu Sunada 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 2012-12-23 with Mathematics categories.
Geometry in ancient Greece is said to have originated in the curiosity of mathematicians about the shapes of crystals, with that curiosity culminating in the classification of regular convex polyhedra addressed in the final volume of Euclid’s Elements. Since then, geometry has taken its own path and the study of crystals has not been a central theme in mathematics, with the exception of Kepler’s work on snowflakes. Only in the nineteenth century did mathematics begin to play a role in crystallography as group theory came to be applied to the morphology of crystals. This monograph follows the Greek tradition in seeking beautiful shapes such as regular convex polyhedra. The primary aim is to convey to the reader how algebraic topology is effectively used to explore the rich world of crystal structures. Graph theory, homology theory, and the theory of covering maps are employed to introduce the notion of the topological crystal which retains, in the abstract, all the information on the connectivity of atoms in the crystal. For that reason the title Topological Crystallography has been chosen. Topological crystals can be described as “living in the logical world, not in space,” leading to the question of how to place or realize them “canonically” in space. Proposed here is the notion of standard realizations of topological crystals in space, including as typical examples the crystal structures of diamond and lonsdaleite. A mathematical view of the standard realizations is also provided by relating them to asymptotic behaviors of random walks and harmonic maps. Furthermore, it can be seen that a discrete analogue of algebraic geometry is linked to the standard realizations. Applications of the discussions in this volume include not only a systematic enumeration of crystal structures, an area of considerable scientific interest for many years, but also the architectural design of lightweight rigid structures. The reader therefore can see the agreement of theory and practice.