The Oxford Handbook of Random Matrix Theory PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download The Oxford Handbook of Random Matrix Theory PDF full book. Access full book title The Oxford Handbook of Random Matrix Theory by Gernot Akemann. Download full books in PDF and EPUB format.
Author: Gernot Akemann
Publisher: OUP Oxford
ISBN: 9780199574001
Category : Mathematics
Languages : en
Pages : 0
Get Book Here
Book Description
Random matrix theory is applied by physicists and mathematicians to understand phenomena in nature and deep mathematical structures. This book offers a comprehensive look at random matrix theory by leading researchers, including applications inside and outside of physics and mathematics.
Author: Gernot Akemann
Publisher: Oxford Handbooks
ISBN: 9780198744191
Category : Mathematics
Languages : en
Pages : 0
Get Book Here
Book Description
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
ISBN: 3319708856
Category : Science
Languages : en
Pages : 122
Get Book Here
Book Description
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.
ISBN: 1470436485
Category : Mathematics
Languages : en
Pages : 239
Get Book Here
Book Description
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
ISBN: 1108488080
Category : Computers
Languages : en
Pages : 371
Get Book Here
Book Description
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.
ISBN: 0821883577
Category : Mathematics
Languages : en
Pages : 236
Get Book Here
Book Description
"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
ISBN: 1108317995
Category : Mathematics
Languages : en
Pages : 225
Get Book Here
Book Description
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: Joel Tropp
Publisher:
ISBN: 9781601988386
Category : Computers
Languages : en
Pages : 256
Get Book Here
Book Description
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: Terence Tao
Publisher: American Mathematical Soc.
ISBN: 0821874306
Category : Mathematics
Languages : en
Pages : 298
Get Book Here
Book Description
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: Badi Hani Baltagi
Publisher:
ISBN: 0199940045
Category : Business & Economics
Languages : en
Pages : 705
Get Book Here
Book Description
The Oxford Handbook of Panel Data examines new developments in the theory and applications of panel data. It includes basic topics like non-stationary panels, co-integration in panels, multifactor panel models, panel unit roots, measurement error in panels, incidental parameters and dynamic panels, spatial panels, nonparametric panel data, random coefficients, treatment effects, sample selection, count panel data, limited dependent variable panel models, unbalanced panel models with interactive effects and influential observations in panel data. Contributors to the Handbook explore applications of panel data to a wide range of topics in economics, including health, labor, marketing, trade, productivity, and macro applications in panels. This Handbook is an informative and comprehensive guide for both those who are relatively new to the field and for those wishing to extend their knowledge to the frontier. It is a trusted and definitive source on panel data, having been edited by Professor Badi Baltagi-widely recognized as one of the foremost econometricians in the area of panel data econometrics. Professor Baltagi has successfully recruited an all-star cast of experts for each of the well-chosen topics in the Handbook.
Author: Denis Serre
Publisher: Springer Science & Business Media
ISBN: 1441976833
Category : Mathematics
Languages : en
Pages : 291
Get Book Here
Book Description
In this book, Denis Serre begins by providing a clean and concise introduction to the basic theory of matrices. He then goes on to give many interesting applications of matrices to different aspects of mathematics and also other areas of science and engineering. With forty percent new material, this second edition is significantly different from the first edition. Newly added topics include: • Dunford decomposition, • tensor and exterior calculus, polynomial identities, • regularity of eigenvalues for complex matrices, • functional calculus and the Dunford–Taylor formula, • numerical range, • Weyl's and von Neumann’s inequalities, and • Jacobi method with random choice. The book mixes together algebra, analysis, complexity theory and numerical analysis. As such, this book will provide many scientists, not just mathematicians, with a useful and reliable reference. It is intended for advanced undergraduate and graduate students with either applied or theoretical goals. This book is based on a course given by the author at the École Normale Supérieure de Lyon.
