Random Matrix Theory Interacting Particle Systems And Integrable Systems
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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.
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.
Nonlinear Dispersive Partial Differential Equations And Inverse Scattering
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Author : Peter D. Miller
language : en
Publisher: Springer Nature
Release Date : 2019-11-14
Nonlinear Dispersive Partial Differential Equations And Inverse Scattering written by Peter D. Miller and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-14 with Mathematics categories.
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.
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.
Recent Progress In Special Functions
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Author : Galina Filipuk
language : en
Publisher: American Mathematical Society
Release Date : 2024-11-02
Recent Progress In Special Functions written by Galina Filipuk and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-02 with Mathematics categories.
This volume contains a collection of papers that focus on recent research in the broad field of special functions. The articles cover topics related to differential equations, dynamic systems, integrable systems, billiards, and random matrix theory. Linear classical special functions, such as hypergeometric functions, Heun functions, and various orthogonal polynomials and nonlinear special functions (e.g., the Painlev‚ transcendents and their generalizations), are studied from different perspectives. This volume serves as a useful reference for a large audience of mathematicians and mathematical physicists interested in modern theory of special functions. It is suitable for both graduate students and specialists in the field.
Free Probability And Random Matrices
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Author : James A. Mingo
language : en
Publisher: Springer
Release Date : 2017-06-24
Free Probability And Random Matrices written by James A. Mingo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-24 with Mathematics categories.
This volume opens the world of free probability to a wide variety of readers. From its roots in the theory of operator algebras, free probability has intertwined with non-crossing partitions, random matrices, applications in wireless communications, representation theory of large groups, quantum groups, the invariant subspace problem, large deviations, subfactors, and beyond. This book puts a special emphasis on the relation of free probability to random matrices, but also touches upon the operator algebraic, combinatorial, and analytic aspects of the theory. The book serves as a combination textbook/research monograph, with self-contained chapters, exercises scattered throughout the text, and coverage of important ongoing progress of the theory. It will appeal to graduate students and all mathematicians interested in random matrices and free probability from the point of view of operator algebras, combinatorics, analytic functions, or applications in engineering and statistical physics.
An Introduction To Integrable Techniques For One Dimensional Quantum Systems
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Author : Fabio Franchini
language : en
Publisher: Springer
Release Date : 2017-05-25
An Introduction To Integrable Techniques For One Dimensional Quantum Systems written by Fabio Franchini and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-25 with Science categories.
This book introduces the reader to basic notions of integrable techniques for one-dimensional quantum systems. In a pedagogical way, a few examples of exactly solvable models are worked out to go from the coordinate approach to the Algebraic Bethe Ansatz, with some discussion on the finite temperature thermodynamics. The aim is to provide the instruments to approach more advanced books or to allow for a critical reading of research articles and the extraction of useful information from them. We describe the solution of the anisotropic XY spin chain; of the Lieb-Liniger model of bosons with contact interaction at zero and finite temperature; and of the XXZ spin chain, first in the coordinate and then in the algebraic approach. To establish the connection between the latter and the solution of two dimensional classical models, we also introduce and solve the 6-vertex model. Finally, the low energy physics of these integrable models is mapped into the corresponding conformal field theory. Through its style and the choice of topics, this book tries to touch all fundamental ideas behind integrability and is meant for students and researchers interested either in an introduction to later delve in the advance aspects of Bethe Ansatz or in an overview of the topic for broadening their culture.
Tau Functions And Their Applications
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Author : John Harnad
language : en
Publisher: Cambridge University Press
Release Date : 2021-02-04
Tau Functions And Their Applications written by John Harnad 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 2021-02-04 with Mathematics categories.
A thorough introduction to tau functions, from the basics through to the most recent results, with applications in mathematical physics.
Directed Polymers In Random Environments
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Author : Francis Comets
language : en
Publisher: Springer
Release Date : 2017-01-26
Directed Polymers In Random Environments written by Francis Comets and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-26 with Mathematics categories.
Analyzing the phase transition from diffusive to localized behavior in a model of directed polymers in a random environment, this volume places particular emphasis on the localization phenomenon. The main questionis: What does the path of a random walk look like if rewards and penalties are spatially randomly distributed?This model, which provides a simplified version of stretched elastic chains pinned by random impurities, has attracted much research activity, but it (and its relatives) still holds many secrets, especially in high dimensions. It has non-gaussian scaling limits and it belongs to the so-called KPZ universality class when the space is one-dimensional. Adopting a Gibbsian approach, using general and powerful tools from probability theory, the discrete model is studied in full generality. Presenting the state-of-the art from different perspectives, and written in the form of a first course on the subject, this monograph is aimed at researchers in probability or statistical physics, but is also accessible to masters and Ph.D. students.
Games Of No Chance 4
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Author : Richard J. Nowakowski
language : en
Publisher: Cambridge University Press
Release Date : 2015-04-16
Games Of No Chance 4 written by Richard J. Nowakowski 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 2015-04-16 with Mathematics categories.
Combinatorial games are the strategy games that people like to play, for example chess, Hex, and Go. They differ from economic games in that there are two players who play alternately with no hidden cards and no dice. These games have a mathematical structure that allows players to analyse them in the abstract. Games of No Chance 4 contains the first comprehensive explorations of misère (last player to move loses) games, extends the theory for some classes of normal-play (last player to move wins) games and extends the analysis for some specific games. It includes a tutorial for the very successful approach to analysing misère impartial games and the first attempt at using it for misère partisan games. Hex and Go are featured, as well as new games: Toppling Dominoes and Maze. Updated versions of Unsolved Problems in Combinatorial Game Theory and the Combinatorial Games Bibliography complete the volume.