[PDF] An Introduction To Matrix Concentration Inequalities eBook

Author : Joel Tropp
Publisher :
Page : 256 pages
File Size : 34,67 MB
Release : 2015-05-27
Category : Computers
ISBN : 9781601988386

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Random matrices now play a role in many areas of theoretical, applied, and computational mathematics. It is therefore desirable to have tools for studying random matrices that are flexible, easy to use, and powerful. Over the last fifteen years, researchers have developed a remarkable family of results, called matrix concentration inequalities, that achieve all of these goals. This monograph offers an invitation to the field of matrix concentration inequalities. It begins with some history of random matrix theory; it describes a flexible model for random matrices that is suitable for many problems; and it discusses the most important matrix concentration results. To demonstrate the value of these techniques, the presentation includes examples drawn from statistics, machine learning, optimization, combinatorics, algorithms, scientific computing, and beyond.

Author : Joel Aaron Tropp
Publisher :
Page : 230 pages
File Size : 11,37 MB
Release : 2015
Category : Matrix derivatives
ISBN : 9781601988393

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Random matrices now play a role in many areas of theoretical, applied, and computational mathematics. Therefore, it is desirable to have tools for studying random matrices that are flexible, easy to use, and powerful. Over the last fifteen years, researchers have developed a remarkable family of results, called matrix concentration inequalities, that achieve all of these goals. This monograph offers an invitation to the field of matrix concentration inequalities. It begins with some history of random matrix theory; it describes a flexible model for random matrices that is suitable for many problems; and it discusses the most important matrix concentration results. To demonstrate the value of these techniques, the presentation includes examples drawn from statistics, machine learning, optimization, combinatorics, algorithms, scientific computing, and beyond.

Author : Greg W. Anderson
Publisher : Cambridge University Press
Page : 507 pages
File Size : 50,22 MB
Release : 2010
Category : Mathematics
ISBN : 0521194520

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A rigorous introduction to the basic theory of random matrices designed for graduate students with a background in probability theory.

Author : Stéphane Boucheron
Publisher : Oxford University Press
Page : 492 pages
File Size : 22,73 MB
Release : 2013-02-07
Category : Mathematics
ISBN : 0199535256

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Describes the interplay between the probabilistic structure (independence) and a variety of tools ranging from functional inequalities to transportation arguments to information theory. Applications to the study of empirical processes, random projections, random matrix theory, and threshold phenomena are also presented.

Author : Roman Vershynin
Publisher : Cambridge University Press
Page : 299 pages
File Size : 31,9 MB
Release : 2018-09-27
Category : Business & Economics
ISBN : 1108415199

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An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

Author : Alice Guionnet
Publisher : Springer Science & Business Media
Page : 296 pages
File Size : 40,52 MB
Release : 2009-03-25
Category : Mathematics
ISBN : 3540698965

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These lectures emphasize the relation between the problem of enumerating complicated graphs and the related large deviations questions. Such questions are closely related with the asymptotic distribution of matrices.

Author : Elizabeth S. Meckes
Publisher : Cambridge University Press
Page : 225 pages
File Size : 16,34 MB
Release : 2019-08-01
Category : Mathematics
ISBN : 1108317995

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This is the first book to provide a comprehensive overview of foundational results and recent progress in the study of random matrices from the classical compact groups, drawing on the subject's deep connections to geometry, analysis, algebra, physics, and statistics. The book sets a foundation with an introduction to the groups themselves and six different constructions of Haar measure. Classical and recent results are then presented in a digested, accessible form, including the following: results on the joint distributions of the entries; an extensive treatment of eigenvalue distributions, including the Weyl integration formula, moment formulae, and limit theorems and large deviations for the spectral measures; concentration of measure with applications both within random matrix theory and in high dimensional geometry; and results on characteristic polynomials with connections to the Riemann zeta function. This book will be a useful reference for researchers and an accessible introduction for students in related fields.

Author : Terence Tao
Publisher : American Mathematical Soc.
Page : 298 pages
File Size : 27,10 MB
Release : 2012-03-21
Category : Mathematics
ISBN : 0821874306

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The field of random matrix theory has seen an explosion of activity in recent years, with connections to many areas of mathematics and physics. However, this makes the current state of the field almost too large to survey in a single book. In this graduate text, we focus on one specific sector of the field, namely the spectral distribution of random Wigner matrix ensembles (such as the Gaussian Unitary Ensemble), as well as iid matrix ensembles. The text is largely self-contained and starts with a review of relevant aspects of probability theory and linear algebra. With over 200 exercises, the book is suitable as an introductory text for beginning graduate students seeking to enter the field.

Author : Martin J. Wainwright
Publisher : Cambridge University Press
Page : 571 pages
File Size : 33,67 MB
Release : 2019-02-21
Category : Business & Economics
ISBN : 1108498027

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A coherent introductory text from a groundbreaking researcher, focusing on clarity and motivation to build intuition and understanding.

Author : László Erdős
Publisher : American Mathematical Soc.
Page : 239 pages
File Size : 15,27 MB
Release : 2017-08-30
Category : Mathematics
ISBN : 1470436485

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A co-publication of the AMS and the Courant Institute of Mathematical Sciences at New York University This book is a concise and self-contained introduction of recent techniques to prove local spectral universality for large random matrices. Random matrix theory is a fast expanding research area, and this book mainly focuses on the methods that the authors participated in developing over the past few years. Many other interesting topics are not included, and neither are several new developments within the framework of these methods. The authors have chosen instead to present key concepts that they believe are the core of these methods and should be relevant for future applications. They keep technicalities to a minimum to make the book accessible to graduate students. With this in mind, they include in this book the basic notions and tools for high-dimensional analysis, such as large deviation, entropy, Dirichlet form, and the logarithmic Sobolev inequality. This manuscript has been developed and continuously improved over the last five years. The authors have taught this material in several regular graduate courses at Harvard, Munich, and Vienna, in addition to various summer schools and short courses. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.