Random Matrix Theory With An External Source
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Random Matrix Theory With An External Source
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Author : Edouard Brézin
language : en
Publisher: Springer
Release Date : 2017-01-11
Random Matrix Theory With An External Source written by Edouard Brézin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-11 with Science categories.
This is a first book to show that the theory of the Gaussian random matrix is essential to understand the universal correlations with random fluctuations and to demonstrate that it is useful to evaluate topological universal quantities. We consider Gaussian random matrix models in the presence of a deterministic matrix source. In such models the correlation functions are known exactly for an arbitrary source and for any size of the matrices. The freedom given by the external source allows for various tunings to different classes of universality. The main interest is to use this freedom to compute various topological invariants for surfaces such as the intersection numbers for curves drawn on a surface of given genus with marked points, Euler characteristics, and the Gromov–Witten invariants. A remarkable duality for the average of characteristic polynomials is essential for obtaining such topological invariants. The analysis is extended to nonorientable surfaces and to surfaces with boundaries.
A Dynamical Approach To Random Matrix Theory
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Author : László Erdős
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-08-30
A Dynamical Approach To Random Matrix Theory written by László Erdős and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-30 with Random matrices categories.
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.
Introduction To Random Matrices
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Author : Giacomo Livan
language : en
Publisher: Springer
Release Date : 2018-01-16
Introduction To Random Matrices written by Giacomo Livan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-16 with Science categories.
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.
Random Matrix Theory Interacting Particle Systems And Integrable Systems
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Author : Percy Deift
language : en
Publisher: Cambridge University Press
Release Date : 2014-12-15
Random Matrix Theory Interacting Particle Systems And Integrable Systems written by Percy Deift and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-15 with Language Arts & Disciplines categories.
This volume includes review articles and research contributions on long-standing questions on universalities of Wigner matrices and beta-ensembles.
Random Matrices
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Author : Alexei Borodin
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-10-30
Random Matrices written by Alexei Borodin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-30 with Education categories.
Random matrix theory has many roots and many branches in mathematics, statistics, physics, computer science, data science, numerical analysis, biology, ecology, engineering, and operations research. This book provides a snippet of this vast domain of study, with a particular focus on the notations of universality and integrability. Universality shows that many systems behave the same way in their large scale limit, while integrability provides a route to describe the nature of those universal limits. Many of the ten contributed chapters address these themes, while others touch on applications of tools and results from random matrix theory. This book is appropriate for graduate students and researchers interested in learning techniques and results in random matrix theory from different perspectives and viewpoints. It also captures a moment in the evolution of the theory, when the previous decade brought major break-throughs, prompting exciting new directions of research.
A First Course In Random Matrix Theory
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Author : Marc Potters
language : en
Publisher: Cambridge University Press
Release Date : 2020-12-03
A First Course In Random Matrix Theory written by Marc Potters and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-03 with Computers categories.
An intuitive, up-to-date introduction to random matrix theory and free calculus, with real world illustrations and Big Data applications.
The Oxford Handbook Of Random Matrix Theory
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Author : Gernot Akemann
language : en
Publisher: Oxford Handbooks
Release Date : 2015-08-09
The Oxford Handbook Of Random Matrix Theory written by Gernot Akemann and has been published by Oxford Handbooks this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-09 with Mathematics categories.
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.
Topics In Random Matrix Theory
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Author : Terence Tao
language : en
Publisher: American Mathematical Soc.
Release Date : 2012-03-21
Topics In Random Matrix Theory written by Terence Tao and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-21 with Mathematics categories.
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.
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Author :
language : en
Publisher: World Scientific
Release Date :
written by and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Random Matrix Models And Their Applications
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Author : Pavel Bleher
language : en
Publisher: Cambridge University Press
Release Date : 2001-06-04
Random Matrix Models And Their Applications written by Pavel Bleher and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-04 with Mathematics categories.
Expository articles on random matrix theory emphasizing the exchange of ideas between the physical and mathematical communities.