Random Matrix Models And Their Applications PDF Download
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Author | : Pavel Bleher |
Publisher | : Cambridge University Press |
Total Pages | : 454 |
Release | : 2001-06-04 |
Genre | : Mathematics |
ISBN | : 9780521802093 |
Download Random Matrix Models and Their Applications Book in PDF, ePub and Kindle
Expository articles on random matrix theory emphasizing the exchange of ideas between the physical and mathematical communities.
Author | : Édouard Brezin |
Publisher | : Springer Science & Business Media |
Total Pages | : 519 |
Release | : 2006-07-03 |
Genre | : Science |
ISBN | : 140204531X |
Download Applications of Random Matrices in Physics Book in PDF, ePub and Kindle
Random matrices are widely and successfully used in physics for almost 60-70 years, beginning with the works of Dyson and Wigner. Although it is an old subject, it is constantly developing into new areas of physics and mathematics. It constitutes now a part of the general culture of a theoretical physicist. Mathematical methods inspired by random matrix theory become more powerful, sophisticated and enjoy rapidly growing applications in physics. Recent examples include the calculation of universal correlations in the mesoscopic system, new applications in disordered and quantum chaotic systems, in combinatorial and growth models, as well as the recent breakthrough, due to the matrix models, in two dimensional gravity and string theory and the non-abelian gauge theories. The book consists of the lectures of the leading specialists and covers rather systematically many of these topics. It can be useful to the specialists in various subjects using random matrices, from PhD students to confirmed scientists.
Author | : Pavel Bleher |
Publisher | : American Mathematical Soc. |
Total Pages | : 237 |
Release | : 2013-12-04 |
Genre | : Mathematics |
ISBN | : 1470409615 |
Download Random Matrices and the Six-Vertex Model Book in PDF, ePub and Kindle
This book provides a detailed description of the Riemann-Hilbert approach (RH approach) to the asymptotic analysis of both continuous and discrete orthogonal polynomials, and applications to random matrix models as well as to the six-vertex model. The RH approach was an important ingredient in the proofs of universality in unitary matrix models. This book gives an introduction to the unitary matrix models and discusses bulk and edge universality. The six-vertex model is an exactly solvable two-dimensional model in statistical physics, and thanks to the Izergin-Korepin formula for the model with domain wall boundary conditions, its partition function matches that of a unitary matrix model with nonpolynomial interaction. The authors introduce in this book the six-vertex model and include a proof of the Izergin-Korepin formula. Using the RH approach, they explicitly calculate the leading and subleading terms in the thermodynamic asymptotic behavior of the partition function of the six-vertex model with domain wall boundary conditions in all the three phases: disordered, ferroelectric, and antiferroelectric. Titles in this series are co-published with the Centre de Recherches Mathématiques.
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 | : Zhidong Bai |
Publisher | : World Scientific |
Total Pages | : 232 |
Release | : 2014-01-24 |
Genre | : Mathematics |
ISBN | : 9814579076 |
Download Spectral Theory of Large Dimensional Random Matrices and Its Applications to Wireless Communications and Finance Statistics Book in PDF, ePub and Kindle
The book contains three parts: Spectral theory of large dimensional random matrices; Applications to wireless communications; and Applications to finance. In the first part, we introduce some basic theorems of spectral analysis of large dimensional random matrices that are obtained under finite moment conditions, such as the limiting spectral distributions of Wigner matrix and that of large dimensional sample covariance matrix, limits of extreme eigenvalues, and the central limit theorems for linear spectral statistics. In the second part, we introduce some basic examples of applications of random matrix theory to wireless communications and in the third part, we present some examples of Applications to statistical finance. Contents:IntroductionLimiting Spectral DistributionsExtreme EigenvaluesCentral Limit Theorems of Linear Spectral StatisticsLimiting Behavior of Eigenmatrix of Sample Covariance MatrixWireless CommunicationsLimiting Performances of Linear and Iterative ReceiversApplication to Finance Readership: Graduate students and researchers in random matrices. Key Features:The book introduces basic theorems in large dimensional random matrices emphasizing those which are established under moment conditions and are thus applicable to statisticsThe long proofs of some theorems are omitted and their references have been providedExamples of various applications to wireless communications and finance are givenKeywords:Statistical Finance;Random Matrix Theory;Spectral Analysis of Random Matrices;Wireless CommunicationsReviews: “Practitioners looking for an introduction to the applications of random matrix theory to finance will find this part useful.” Mathematical Reviews Clippings
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 | : 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 | : 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 | : 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 | : Greg W. Anderson |
Publisher | : Cambridge University Press |
Total Pages | : 507 |
Release | : 2010 |
Genre | : Mathematics |
ISBN | : 0521194520 |
Download An Introduction to Random Matrices Book in PDF, ePub and Kindle
A rigorous introduction to the basic theory of random matrices designed for graduate students with a background in probability theory.