The Oxford Handbook Of Random Matrix Theory PDF Download
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Author | : Gernot Akemann |
Publisher | : Oxford Handbooks |
Total Pages | : 0 |
Release | : 2015-08-09 |
Genre | : Mathematics |
ISBN | : 9780198744191 |
Download The Oxford Handbook of Random Matrix Theory Book in PDF, ePub and Kindle
With a foreword by Freeman Dyson, the handbook brings together leading mathematicians and physicists to offer a comprehensive overview of random matrix theory, including a guide to new developments and the diverse range of applications of this approach.In part one, all modern and classical techniques of solving random matrix models are explored, including orthogonal polynomials, exact replicas or supersymmetry.
Author | : Giacomo Livan |
Publisher | : Springer |
Total Pages | : 124 |
Release | : 2018-01-16 |
Genre | : Science |
ISBN | : 3319708856 |
Download Introduction to Random Matrices Book in PDF, ePub and Kindle
Modern developments of Random Matrix Theory as well as pedagogical approaches to the standard core of the discipline are surprisingly hard to find in a well-organized, readable and user-friendly fashion. This slim and agile book, written in a pedagogical and hands-on style, without sacrificing formal rigor fills this gap. It brings Ph.D. students in Physics, as well as more senior practitioners, through the standard tools and results on random matrices, with an eye on most recent developments that are not usually covered in introductory texts. The focus is mainly on random matrices with real spectrum.The main guiding threads throughout the book are the Gaussian Ensembles. In particular, Wigner’s semicircle law is derived multiple times to illustrate several techniques (e.g., Coulomb gas approach, replica theory).Most chapters are accompanied by Matlab codes (stored in an online repository) to guide readers through the numerical check of most analytical results.
Author | : László Erdős |
Publisher | : American Mathematical Soc. |
Total Pages | : 226 |
Release | : 2017-08-30 |
Genre | : Random matrices |
ISBN | : 1470436485 |
Download A Dynamical Approach to Random Matrix Theory Book in PDF, ePub and Kindle
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.
Author | : Marc Potters |
Publisher | : Cambridge University Press |
Total Pages | : 371 |
Release | : 2020-12-03 |
Genre | : Computers |
ISBN | : 1108488080 |
Download A First Course in Random Matrix Theory Book in PDF, ePub and Kindle
An intuitive, up-to-date introduction to random matrix theory and free calculus, with real world illustrations and Big Data applications.
Author | : Percy Deift |
Publisher | : American Mathematical Soc. |
Total Pages | : 236 |
Release | : 2009-01-01 |
Genre | : Mathematics |
ISBN | : 0821883577 |
Download Random Matrix Theory Book in PDF, ePub and Kindle
"This book features a unified derivation of the mathematical theory of the three classical types of invariant random matrix ensembles-orthogonal, unitary, and symplectic. The authors follow the approach of Tracy and Widom, but the exposition here contains a substantial amount of additional material, in particular, facts from functional analysis and the theory of Pfaffians. The main result in the book is a proof of universality for orthogonal and symplectic ensembles corresponding to generalized Gaussian type weights following the authors' prior work. New, quantitative error estimates are derived." --Book Jacket.
Author | : Elizabeth S. Meckes |
Publisher | : Cambridge University Press |
Total Pages | : 225 |
Release | : 2019-08-01 |
Genre | : Mathematics |
ISBN | : 1108317995 |
Download The Random Matrix Theory of the Classical Compact Groups Book in PDF, ePub and Kindle
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 | : Marc Potters |
Publisher | : Cambridge University Press |
Total Pages | : 371 |
Release | : 2020-12-03 |
Genre | : Science |
ISBN | : 1108858279 |
Download A First Course in Random Matrix Theory Book in PDF, ePub and Kindle
The real world is perceived and broken down as data, models and algorithms in the eyes of physicists and engineers. Data is noisy by nature and classical statistical tools have so far been successful in dealing with relatively smaller levels of randomness. The recent emergence of Big Data and the required computing power to analyse them have rendered classical tools outdated and insufficient. Tools such as random matrix theory and the study of large sample covariance matrices can efficiently process these big data sets and help make sense of modern, deep learning algorithms. Presenting an introductory calculus course for random matrices, the book focusses on modern concepts in matrix theory, generalising the standard concept of probabilistic independence to non-commuting random variables. Concretely worked out examples and applications to financial engineering and portfolio construction make this unique book an essential tool for physicists, engineers, data analysts, and economists.
Author | : Terence Tao |
Publisher | : American Mathematical Society |
Total Pages | : 296 |
Release | : 2023-08-24 |
Genre | : Mathematics |
ISBN | : 147047459X |
Download Topics in Random Matrix Theory Book in PDF, ePub and Kindle
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 | : Joel Tropp |
Publisher | : |
Total Pages | : 256 |
Release | : 2015-05-27 |
Genre | : Computers |
ISBN | : 9781601988386 |
Download An Introduction to Matrix Concentration Inequalities Book in PDF, ePub and Kindle
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 | : Badi Hani Baltagi |
Publisher | : Oxford Handbooks |
Total Pages | : 705 |
Release | : 2015 |
Genre | : Business & Economics |
ISBN | : 0199940045 |
Download The Oxford Handbook of Panel Data Book in PDF, ePub and Kindle
Panel data econometrics has evolved rapidly over the past three decades. The field is of both theoretical and practical importance, and methods to deal with micro- and macroeconomic panel data are in high demand from practitioners. Applications in finance, development, trade, marketing, health, labor, and consumer economics attest to the usefulness of these methods in applied economics. THis book is a comprehensive source on panel data. It contains 20 chapters edited by Professor Badi Baltagi--one of the leading econometricians in the area of panel data econometrics--and authored by renowned experts in the field. The chapters are divided into two sections. Part I examines new developments in theory. It includes panel cointegration, dynamic panel data models, incidental parameters and dynamic panel modeling, and panel data models for discrete choice. The chapters in Part II target applications of panel data, including health, labor, marketing, trade, productivity and macro applications in panels.