Random Matrix Theory With An External Source PDF Download
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| Author | : Edouard Brézin |
| Publisher | : Springer |
| Total Pages | : 138 |
| Release | : 2017-01-11 |
| Genre | : Science |
| ISBN | : 9811033161 |
Download Random Matrix Theory with an External Source Book in PDF, ePub and Kindle
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.
| 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 | : 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 | : Percy Deift |
| Publisher | : Cambridge University Press |
| Total Pages | : 539 |
| Release | : 2014-12-15 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 1107079926 |
Download Random Matrix Theory, Interacting Particle Systems and Integrable Systems Book in PDF, ePub and Kindle
This volume includes review articles and research contributions on long-standing questions on universalities of Wigner matrices and beta-ensembles.
| 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 | : Jinho Baik |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 461 |
| Release | : 2016-06-22 |
| Genre | : Combinatorial analysis |
| ISBN | : 0821848410 |
Download Combinatorics and Random Matrix Theory Book in PDF, ePub and Kindle
Over the last fifteen years a variety of problems in combinatorics have been solved in terms of random matrix theory. More precisely, the situation is as follows: the problems at hand are probabilistic in nature and, in an appropriate scaling limit, it turns out that certain key quantities associated with these problems behave statistically like the eigenvalues of a (large) random matrix. Said differently, random matrix theory provides a “stochastic special function theory” for a broad and growing class of problems in combinatorics. The goal of this book is to analyze in detail two key examples of this phenomenon, viz., Ulam's problem for increasing subsequences of random permutations and domino tilings of the Aztec diamond. Other examples are also described along the way, but in less detail. Techniques from many different areas in mathematics are needed to analyze these problems. These areas include combinatorics, probability theory, functional analysis, complex analysis, and the theory of integrable systems. The book is self-contained, and along the way we develop enough of the theory we need from each area that a general reader with, say, two or three years experience in graduate school can learn the subject directly from the text.
| Author | : |
| Publisher | : World Scientific |
| Total Pages | : 1001 |
| Release | : |
| Genre | : |
| ISBN | : |
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| Author | : Alexei Borodin |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 498 |
| Release | : 2019-10-30 |
| Genre | : Education |
| ISBN | : 1470452804 |
Download Random Matrices Book in PDF, ePub and Kindle
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.
| Author | : Leonid Andreevich Pastur |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 650 |
| Release | : 2011 |
| Genre | : Mathematics |
| ISBN | : 082185285X |
Download Eigenvalue Distribution of Large Random Matrices Book in PDF, ePub and Kindle
Random matrix theory is a wide and growing field with a variety of concepts, results, and techniques and a vast range of applications in mathematics and the related sciences. The book, written by well-known experts, offers beginners a fairly balanced collection of basic facts and methods (Part 1 on classical ensembles) and presents experts with an exposition of recent advances in the subject (Parts 2 and 3 on invariant ensembles and ensembles with independent entries). The text includes many of the authors' results and methods on several main aspects of the theory, thus allowing them to present a unique and personal perspective on the subject and to cover many topics using a unified approach essentially based on the Stieltjes transform and orthogonal polynomials. The exposition is supplemented by numerous comments, remarks, and problems. This results in a book that presents a detailed and self-contained treatment of the basic random matrix ensembles and asymptotic regimes. This book will be an important reference for researchers in a variety of areas of mathematics and mathematical physics. Various chapters of the book can be used for graduate courses; the main prerequisite is a basic knowledge of calculus, linear algebra, and probability theory.
| Author | : Zhaoben Fang |
| Publisher | : World Scientific |
| Total Pages | : 233 |
| 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: Random Matrix Theory And Its Applications 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.
