Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Random Matrix Theory Interacting Particle Systems And Integrable Systems PDF full book. Access full book title Random Matrix Theory Interacting Particle Systems And Integrable Systems.
| Author | : Percy Deift |
| Publisher | : Cambridge University Press |
| Total Pages | : 539 |
| Release | : 2014-12-15 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 1107079926 |
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 |
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 | : Yuanyuan Xu |
| Publisher | : |
| Total Pages | : |
| Release | : 2018 |
| Genre | : |
| ISBN | : 9780438290754 |
Random Matrix Theory(RMT) is a fast developing area of modern Mathematics with deep connections to Probability, Statistical Mechanics, Quantum Theory, Number Theory, Statistics, and Integrable Systems. In the first part of my dissertation, I consider an interacting particle system on the unit circle with stronger repulsion than that of the Circular beta Ensemble in RMT and prove the Gaussian approximation of the distribution of the particles. In addition, the Central Limit Theorem(CLT) for the linear statistics of the particles is obtained as a corollary. In the second part of the dissertation, I consider the orthogonal group SO(2n) with the Haar measure and prove the CLT for the linear eigenvalue statistics in the mesoscopic regime where the test function depends on n. The results can be generalized to other classic compact groups, such as SO(2n+1) and Sp(n).
| Author | : Jinho Baik |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 448 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 0821842404 |
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 | : Richard Durrett |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 394 |
| Release | : 1985 |
| Genre | : Mathematics |
| ISBN | : 0821850423 |
Covers the proceedings of the 1984 AMS Summer Research Conference. This work provides a summary of results from some of the areas in probability theory; interacting particle systems, percolation, random media (bulk properties and hydrodynamics), the Ising model and large deviations.
| Author | : Zhidong Bai |
| Publisher | : World Scientific |
| Total Pages | : 176 |
| Release | : 2009-07-27 |
| Genre | : Mathematics |
| ISBN | : 9814467995 |
Random matrix theory has a long history, beginning in the first instance in multivariate statistics. It was used by Wigner to supply explanations for the important regularity features of the apparently random dispositions of the energy levels of heavy nuclei. The subject was further deeply developed under the important leadership of Dyson, Gaudin and Mehta, and other mathematical physicists.In the early 1990s, random matrix theory witnessed applications in string theory and deep connections with operator theory, and the integrable systems were established by Tracy and Widom. More recently, the subject has seen applications in such diverse areas as large dimensional data analysis and wireless communications.This volume contains chapters written by the leading participants in the field which will serve as a valuable introduction into this very exciting area of research.
| Author | : Pavel Bleher |
| Publisher | : Cambridge University Press |
| Total Pages | : 454 |
| Release | : 2001-06-04 |
| Genre | : Mathematics |
| ISBN | : 9780521802093 |
Expository articles on random matrix theory emphasizing the exchange of ideas between the physical and mathematical communities.
| Author | : Marc Potters |
| Publisher | : Cambridge University Press |
| Total Pages | : 371 |
| Release | : 2020-12-03 |
| Genre | : Computers |
| ISBN | : 1108488080 |
An intuitive, up-to-date introduction to random matrix theory and free calculus, with real world illustrations and Big Data applications.
| Author | : Alexei Borodin |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 498 |
| Release | : 2019-10-30 |
| Genre | : Education |
| ISBN | : 1470452804 |
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 | : Peter D. Miller |
| Publisher | : Springer Nature |
| Total Pages | : 528 |
| Release | : 2019-11-14 |
| Genre | : Mathematics |
| ISBN | : 1493998064 |
This volume contains lectures and invited papers from the Focus Program on "Nonlinear Dispersive Partial Differential Equations and Inverse Scattering" held at the Fields Institute from July 31-August 18, 2017. The conference brought together researchers in completely integrable systems and PDE with the goal of advancing the understanding of qualitative and long-time behavior in dispersive nonlinear equations. The program included Percy Deift’s Coxeter lectures, which appear in this volume together with tutorial lectures given during the first week of the focus program. The research papers collected here include new results on the focusing nonlinear Schrödinger (NLS) equation, the massive Thirring model, and the Benjamin-Bona-Mahoney equation as dispersive PDE in one space dimension, as well as the Kadomtsev-Petviashvili II equation, the Zakharov-Kuznetsov equation, and the Gross-Pitaevskii equation as dispersive PDE in two space dimensions. The Focus Program coincided with the fiftieth anniversary of the discovery by Gardner, Greene, Kruskal and Miura that the Korteweg-de Vries (KdV) equation could be integrated by exploiting a remarkable connection between KdV and the spectral theory of Schrodinger's equation in one space dimension. This led to the discovery of a number of completely integrable models of dispersive wave propagation, including the cubic NLS equation, and the derivative NLS equation in one space dimension and the Davey-Stewartson, Kadomtsev-Petviashvili and Novikov-Veselov equations in two space dimensions. These models have been extensively studied and, in some cases, the inverse scattering theory has been put on rigorous footing. It has been used as a powerful analytical tool to study global well-posedness and elucidate asymptotic behavior of the solutions, including dispersion, soliton resolution, and semiclassical limits.
