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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 | : Jinho Baik |
Publisher | : American Mathematical Soc. |
Total Pages | : 448 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 0821842404 |
Download Integrable Systems and Random Matrices Book in PDF, ePub and Kindle
This volume contains the proceedings of a conference held at the Courant Institute in 2006 to celebrate the 60th birthday of Percy A. Deift. The program reflected the wide-ranging contributions of Professor Deift to analysis with emphasis on recent developments in Random Matrix Theory and integrable systems. The articles in this volume present a broad view on the state of the art in these fields. Topics on random matrices include the distributions and stochastic processes associated with local eigenvalue statistics, as well as their appearance in combinatorial models such as TASEP, last passage percolation and tilings. The contributions in integrable systems mostly deal with focusing NLS, the Camassa-Holm equation and the Toda lattice. A number of papers are devoted to techniques that are used in both fields. These techniques are related to orthogonal polynomials, operator determinants, special functions, Riemann-Hilbert problems, direct and inverse spectral theory. Of special interest is the article of Percy Deift in which he discusses some open problems of Random Matrix Theory and the theory of integrable systems.
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 | : M. Bertola |
Publisher | : |
Total Pages | : 285 |
Release | : 2006 |
Genre | : Mathematical physics |
ISBN | : |
Download Special Issue on Random Matrices and Integrable Systems Book in PDF, ePub and Kindle
Author | : Anton Dzhamay |
Publisher | : American Mathematical Soc. |
Total Pages | : 363 |
Release | : 2013-06-26 |
Genre | : Mathematics |
ISBN | : 0821887475 |
Download Algebraic and Geometric Aspects of Integrable Systems and Random Matrices Book in PDF, ePub and Kindle
This volume contains the proceedings of the AMS Special Session on Algebraic and Geometric Aspects of Integrable Systems and Random Matrices, held from January 6-7, 2012, in Boston, MA. The very wide range of topics represented in this volume illustrates
Author | : Jinho Baik |
Publisher | : American Mathematical Soc. |
Total Pages | : 478 |
Release | : 2016-06-22 |
Genre | : Mathematics |
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 | : Jinho Baik |
Publisher | : |
Total Pages | : 448 |
Release | : 2008 |
Genre | : Hamiltonian systems |
ISBN | : |
Download Integrable Systems and Random Matrices Book in PDF, ePub and Kindle
Author | : László Erdős |
Publisher | : American Mathematical Soc. |
Total Pages | : 239 |
Release | : 2017-08-30 |
Genre | : Mathematics |
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 | : Marta Dell'Atti |
Publisher | : |
Total Pages | : |
Release | : 2021 |
Genre | : |
ISBN | : |
Download Integrable Systems, Random Matrices and Applications Book in PDF, ePub and Kindle
Author | : |
Publisher | : |
Total Pages | : 430 |
Release | : 2007 |
Genre | : |
ISBN | : 9780821841297 |
Download Integrable Systems and Random Matrices Book in PDF, ePub and Kindle