Asymptotic Geometric Analysis PDF Download
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Author | : Shiri Artstein-Avidan |
Publisher | : American Mathematical Society |
Total Pages | : 645 |
Release | : 2021-12-13 |
Genre | : Mathematics |
ISBN | : 1470463601 |
Download Asymptotic Geometric Analysis, Part II Book in PDF, ePub and Kindle
This book is a continuation of Asymptotic Geometric Analysis, Part I, which was published as volume 202 in this series. Asymptotic geometric analysis studies properties of geometric objects, such as normed spaces, convex bodies, or convex functions, when the dimensions of these objects increase to infinity. The asymptotic approach reveals many very novel phenomena which influence other fields in mathematics, especially where a large data set is of main concern, or a number of parameters which becomes uncontrollably large. One of the important features of this new theory is in developing tools which allow studying high parametric families. Among the topics covered in the book are measure concentration, isoperimetric constants of log-concave measures, thin-shell estimates, stochastic localization, the geometry of Gaussian measures, volume inequalities for convex bodies, local theory of Banach spaces, type and cotype, the Banach-Mazur compactum, symmetrizations, restricted invertibility, and functional versions of geometric notions and inequalities.
Author | : Monika Ludwig |
Publisher | : Springer Science & Business Media |
Total Pages | : 402 |
Release | : 2013-03-27 |
Genre | : Mathematics |
ISBN | : 1461464064 |
Download Asymptotic Geometric Analysis Book in PDF, ePub and Kindle
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.
Author | : |
Publisher | : |
Total Pages | : |
Release | : 2015 |
Genre | : |
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Download Asymptotic Geometric Analysis Book in PDF, ePub and Kindle
Author | : Guillaume Aubrun |
Publisher | : American Mathematical Society |
Total Pages | : 439 |
Release | : 2024-07-29 |
Genre | : Mathematics |
ISBN | : 1470477963 |
Download Alice and Bob Meet Banach Book in PDF, ePub and Kindle
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.
Author | : Shiri Artstein-Avidan |
Publisher | : American Mathematical Soc. |
Total Pages | : 473 |
Release | : 2015-06-18 |
Genre | : Mathematics |
ISBN | : 1470421933 |
Download Asymptotic Geometric Analysis, Part I Book in PDF, ePub and Kindle
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.
Author | : Guillaume Aubrun |
Publisher | : American Mathematical Soc. |
Total Pages | : 442 |
Release | : 2017-08-30 |
Genre | : Mathematics |
ISBN | : 1470434687 |
Download Alice and Bob Meet Banach Book in PDF, ePub and Kindle
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.
Author | : Michael A. Roysdon |
Publisher | : |
Total Pages | : 0 |
Release | : 2020 |
Genre | : |
ISBN | : |
Download On Some Geometric and Functional Inequalities in Asymptotic Geometric Analysis Book in PDF, ePub and Kindle
This dissertation concerns geometric and functional inequalities arising in the areas of convex geometry, asymptotic geometric analysis, and measure theory.
Author | : Keith M. Ball |
Publisher | : Cambridge University Press |
Total Pages | : 260 |
Release | : 1999-01-28 |
Genre | : Mathematics |
ISBN | : 9780521642590 |
Download Convex Geometric Analysis Book in PDF, ePub and Kindle
Articles on classical convex geometry, geometric functional analysis, computational geometry, and related areas of harmonic analysis, first published in 1999.
Author | : Vitali D. Milman |
Publisher | : Springer |
Total Pages | : 299 |
Release | : 2004-08-30 |
Genre | : Mathematics |
ISBN | : 3540444890 |
Download Geometric Aspects of Functional Analysis Book in PDF, ePub and Kindle
The Israeli GAFA seminar (on Geometric Aspect of Functional Analysis) during the years 2002-2003 follows the long tradition of the previous volumes. It reflects the general trends of the theory. Most of the papers deal with different aspects of the Asymptotic Geometric Analysis. In addition the volume contains papers on related aspects of Probability, classical Convexity and also Partial Differential Equations and Banach Algebras. There are also two expository papers on topics which proved to be very much related to the main topic of the seminar. One is Statistical Learning Theory and the other is Models of Statistical Physics. All the papers of this collection are original research papers.
Author | : Victor Guillemin |
Publisher | : American Mathematical Soc. |
Total Pages | : 500 |
Release | : 1990 |
Genre | : Mathematics |
ISBN | : 0821816330 |
Download Geometric Asymptotics Book in PDF, ePub and Kindle
Symplectic geometry and the theory of Fourier integral operators are modern manifestations of themes that have occupied a central position in mathematical thought for the past three hundred years--the relations between the wave and the corpuscular theories of light. The purpose of this book is to develop these themes, and present some of the recent advances, using the language of differential geometry as a unifying influence.