Random Matrix Theory With An External Source PDF Download
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Author | : Edouard Brézin |
Publisher | : Springer |
Total Pages | : 143 |
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 | : 122 |
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 | : Antonia M. Tulino |
Publisher | : Now Publishers Inc |
Total Pages | : 196 |
Release | : 2004 |
Genre | : Computers |
ISBN | : 9781933019000 |
Download Random Matrix Theory and Wireless Communications Book in PDF, ePub and Kindle
Random Matrix Theory and Wireless Communications is the first tutorial on random matrices which provides an overview of the theory and brings together in one source the most significant results recently obtained.
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 | : 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 | : Terence Tao |
Publisher | : American Mathematical Soc. |
Total Pages | : 298 |
Release | : 2012-03-21 |
Genre | : Mathematics |
ISBN | : 0821874306 |
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 | : |
Publisher | : World Scientific |
Total Pages | : 1001 |
Release | : |
Genre | : |
ISBN | : |
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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 | : John Harnad |
Publisher | : Springer Science & Business Media |
Total Pages | : 536 |
Release | : 2011-05-06 |
Genre | : Science |
ISBN | : 1441995145 |
Download Random Matrices, Random Processes and Integrable Systems Book in PDF, ePub and Kindle
This book explores the remarkable connections between two domains that, a priori, seem unrelated: Random matrices (together with associated random processes) and integrable systems. The relations between random matrix models and the theory of classical integrable systems have long been studied. These appear mainly in the deformation theory, when parameters characterizing the measures or the domain of localization of the eigenvalues are varied. The resulting differential equations determining the partition function and correlation functions are, remarkably, of the same type as certain equations appearing in the theory of integrable systems. They may be analyzed effectively through methods based upon the Riemann-Hilbert problem of analytic function theory and by related approaches to the study of nonlinear asymptotics in the large N limit. Associated with studies of matrix models are certain stochastic processes, the "Dyson processes", and their continuum diffusion limits, which govern the spectrum in random matrix ensembles, and may also be studied by related methods. Random Matrices, Random Processes and Integrable Systems provides an in-depth examination of random matrices with applications over a vast variety of domains, including multivariate statistics, random growth models, and many others. Leaders in the field apply the theory of integrable systems to the solution of fundamental problems in random systems and processes using an interdisciplinary approach that sheds new light on a dynamic topic of current research.
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.