Random Matrices And The Six Vertex Model

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Random Matrices and the Six-Vertex Model

Pavel Bleher, Karl Liechty
Random Matrices and the Six Vertex Model Book PDF

Author : Pavel Bleher, Karl Liechty
Publisher : American Mathematical Soc.
Page : 237 pages
File Size : 55,6 Mb
Release : 2013-12-04
Category : Mathematics
ISBN : 9781470409616

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Random Matrices and the Six-Vertex Model by Pavel Bleher, Karl Liechty Pdf

This book provides a detailed description of the Riemann-Hilbert approach (RH approach) to the asymptotic analysis of both continuous and discrete orthogonal polynomials, and applications to random matrix models as well as to the six-vertex model. The RH approach was an important ingredient in the proofs of universality in unitary matrix models. This book gives an introduction to the unitary matrix models and discusses bulk and edge universality. The six-vertex model is an exactly solvable two-dimensional model in statistical physics, and thanks to the Izergin-Korepin formula for the model with domain wall boundary conditions, its partition function matches that of a unitary matrix model with nonpolynomial interaction. The authors introduce in this book the six-vertex model and include a proof of the Izergin-Korepin formula. Using the RH approach, they explicitly calculate the leading and subleading terms in the thermodynamic asymptotic behavior of the partition function of the six-vertex model with domain wall boundary conditions in all the three phases: disordered, ferroelectric, and antiferroelectric. Titles in this series are co-published with the Centre de Recherches Mathématiques.

Random Matrix Theory, Interacting Particle Systems and Integrable Systems

Percy Deift,Peter Forrester
Random Matrix Theory Interacting Particle Systems and Integrable Systems Book PDF

Author : Percy Deift,Peter Forrester
Publisher : Cambridge University Press
Page : 539 pages
File Size : 43,5 Mb
Release : 2014-12-15
Category : Language Arts & Disciplines
ISBN : 9781107079922

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Random Matrix Theory, Interacting Particle Systems and Integrable Systems by Percy Deift,Peter Forrester Pdf

This volume includes review articles and research contributions on long-standing questions on universalities of Wigner matrices and beta-ensembles.

Integrable Systems and Random Matrices

Jinho Baik
Integrable Systems and Random Matrices Book PDF

Author : Jinho Baik
Publisher : American Mathematical Soc.
Page : 448 pages
File Size : 44,6 Mb
Release : 2008
Category : Mathematics
ISBN : 9780821842409

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Integrable Systems and Random Matrices by Jinho Baik Pdf

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.

Stochastic Processes and Random Matrices

Gregory Schehr,Yan V. Fyodorov,Alexander Altland,Neil O'Connell,Leticia F. Cugliandolo
Stochastic Processes and Random Matrices Book PDF

Author : Gregory Schehr,Yan V. Fyodorov,Alexander Altland,Neil O'Connell,Leticia F. Cugliandolo
Publisher : Oxford University Press
Page : 641 pages
File Size : 46,8 Mb
Release : 2017
Category : Mathematics
ISBN : 9780198797319

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Stochastic Processes and Random Matrices by Gregory Schehr,Yan V. Fyodorov,Alexander Altland,Neil O'Connell,Leticia F. Cugliandolo Pdf

This text covers in detail recent developments in the field of stochastic processes and Random Matrix Theory. Matrix models have been playing an important role in theoretical physics for a long time and are currently also a very active domain of research in mathematics.

Toeplitz Operators and Random Matrices

Estelle Basor,Albrecht Böttcher,Torsten Ehrhardt,Craig A. Tracy
Toeplitz Operators and Random Matrices Book PDF

Author : Estelle Basor,Albrecht Böttcher,Torsten Ehrhardt,Craig A. Tracy
Publisher : Springer Nature
Page : 606 pages
File Size : 43,5 Mb
Release : 2023-01-01
Category : Mathematics
ISBN : 9783031138515

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Toeplitz Operators and Random Matrices by Estelle Basor,Albrecht Böttcher,Torsten Ehrhardt,Craig A. Tracy Pdf

This volume is dedicated to the memory of Harold Widom (1932–2021), an outstanding mathematician who has enriched mathematics with his ideas and ground breaking work since the 1950s until the present time. It contains a biography of Harold Widom, personal notes written by his former students or colleagues, and also his last, previously unpublished paper on domain walls in a Heisenberg–Ising chain. Widom's most famous contributions were made to Toeplitz operators and random matrices. While his work on random matrices is part of almost all the present-day research activities in this field, his work in Toeplitz operators and matrices was done mainly before 2000 and is therefore described in a contribution devoted to his achievements in just this area. The volume contains 18 invited and refereed research and expository papers on Toeplitz operators and random matrices. These present new results or new perspectives on topics related to Widom's work.

Random Matrix Models and Their Applications

Pavel Bleher,Alexander Its
Random Matrix Models and Their Applications Book PDF

Author : Pavel Bleher,Alexander Its
Publisher : Cambridge University Press
Page : 454 pages
File Size : 54,9 Mb
Release : 2001-06-04
Category : Mathematics
ISBN : 0521802091

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Random Matrix Models and Their Applications by Pavel Bleher,Alexander Its Pdf

Expository articles on random matrix theory emphasizing the exchange of ideas between the physical and mathematical communities.

New Trends in Mathematical Physics

Vladas Sidoravicius
New Trends in Mathematical Physics Book PDF

Author : Vladas Sidoravicius
Publisher : Springer Science & Business Media
Page : 886 pages
File Size : 50,8 Mb
Release : 2009-08-31
Category : Science
ISBN : 9789048128105

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New Trends in Mathematical Physics by Vladas Sidoravicius Pdf

This book collects selected papers written by invited and plenary speakers of the 15th International Congress on Mathematical Physics (ICMP) in the aftermath of the conference. In extensive review articles and expository texts as well as advanced research articles the world leading experts present the state of the art in modern mathematical physics. New mathematical concepts and ideas are introduced by prominent mathematicalphysicists and mathematicians, covering among others the fields of Dynamical Systems, Operator Algebras, Partial Differential Equations, Probability Theory, Random Matrices, Condensed Matter Physics, Statistical Mechanics, General Relativity, Quantum Mechanics, Quantum Field Theory, Quantum Information and String Theory. All together the contributions in this book give a panoramic view of the latest developments in mathematical physics. They will help readers with a general interest in mathematical physics to get an update on the most recent developments in their field, and give a broad overview on actual and future research directions in this fascinating and rapidly expanding area.

Introduction to Random Matrices

Giacomo Livan,Marcel Novaes,Pierpaolo Vivo
Introduction to Random Matrices Book PDF

Author : Giacomo Livan,Marcel Novaes,Pierpaolo Vivo
Publisher : Springer
Page : 124 pages
File Size : 54,8 Mb
Release : 2018-01-16
Category : Science
ISBN : 9783319708850

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Introduction to Random Matrices by Giacomo Livan,Marcel Novaes,Pierpaolo Vivo Pdf

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.

Random Matrices, Random Processes and Integrable Systems

John Harnad
Random Matrices Random Processes and Integrable Systems Book PDF

Author : John Harnad
Publisher : Springer Science & Business Media
Page : 536 pages
File Size : 40,5 Mb
Release : 2011-05-06
Category : Science
ISBN : 9781441995148

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Random Matrices, Random Processes and Integrable Systems by John Harnad Pdf

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.

Random Walks, Boundaries and Spectra

Daniel Lenz,Florian Sobieczky,Wolfgang Woess
Random Walks Boundaries and Spectra Book PDF

Author : Daniel Lenz,Florian Sobieczky,Wolfgang Woess
Publisher : Springer Science & Business Media
Page : 345 pages
File Size : 42,8 Mb
Release : 2011-06-16
Category : Mathematics
ISBN : 9783034602440

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Random Walks, Boundaries and Spectra by Daniel Lenz,Florian Sobieczky,Wolfgang Woess Pdf

These proceedings represent the current state of research on the topics 'boundary theory' and 'spectral and probability theory' of random walks on infinite graphs. They are the result of the two workshops held in Styria (Graz and St. Kathrein am Offenegg, Austria) between June 29th and July 5th, 2009. Many of the participants joined both meetings. Even though the perspectives range from very different fields of mathematics, they all contribute with important results to the same wonderful topic from structure theory, which, by extending a quotation of Laurent Saloff-Coste, could be described by 'exploration of groups by random processes'.

Classification and Identification of Lie Algebras

Libor Šnob,Pavel Winternitz
Classification and Identification of Lie Algebras Book PDF

Author : Libor Šnob,Pavel Winternitz
Publisher : American Mathematical Soc.
Page : 306 pages
File Size : 54,5 Mb
Release : 2017-04-05
Category : Electronic
ISBN : 9781470436544

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Classification and Identification of Lie Algebras by Libor Šnob,Pavel Winternitz Pdf

The purpose of this book is to serve as a tool for researchers and practitioners who apply Lie algebras and Lie groups to solve problems arising in science and engineering. The authors address the problem of expressing a Lie algebra obtained in some arbitrary basis in a more suitable basis in which all essential features of the Lie algebra are directly visible. This includes algorithms accomplishing decomposition into a direct sum, identification of the radical and the Levi decomposition, and the computation of the nilradical and of the Casimir invariants. Examples are given for each algorithm. For low-dimensional Lie algebras this makes it possible to identify the given Lie algebra completely. The authors provide a representative list of all Lie algebras of dimension less or equal to 6 together with their important properties, including their Casimir invariants. The list is ordered in a way to make identification easy, using only basis independent properties of the Lie algebras. They also describe certain classes of nilpotent and solvable Lie algebras of arbitrary finite dimensions for which complete or partial classification exists and discuss in detail their construction and properties. The book is based on material that was previously dispersed in journal articles, many of them written by one or both of the authors together with their collaborators. The reader of this book should be familiar with Lie algebra theory at an introductory level.

The Geometric and Arithmetic Volume of Shimura Varieties of Orthogonal Type

Fritz Hörmann
The Geometric and Arithmetic Volume of Shimura Varieties of Orthogonal Type Book PDF

Author : Fritz Hörmann
Publisher : American Mathematical Society
Page : 162 pages
File Size : 52,8 Mb
Release : 2014-11-05
Category : Mathematics
ISBN : 9781470419127

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The Geometric and Arithmetic Volume of Shimura Varieties of Orthogonal Type by Fritz Hörmann Pdf

This book outlines a functorial theory of integral models of (mixed) Shimura varieties and of their toroidal compactifications, for odd primes of good reduction. This is the integral version, developed in the author's thesis, of the theory invented by Deligne and Pink in the rational case. In addition, the author develops a theory of arithmetic Chern classes of integral automorphic vector bundles with singular metrics using the work of Burgos, Kramer and Kühn. The main application is calculating arithmetic volumes or "heights" of Shimura varieties of orthogonal type using Borcherds' famous modular forms with their striking product formula--an idea due to Bruinier-Burgos-Kühn and Kudla. This should be seen as an Arakelov analogue of the classical calculation of volumes of orthogonal locally symmetric spaces by Siegel and Weil. In the latter theory, the volumes are related to special values of (normalized) Siegel Eisenstein series. In this book, it is proved that the Arakelov analogues are related to special derivatives of such Eisenstein series. This result gives substantial evidence in the direction of Kudla's conjectures in arbitrary dimensions. The validity of the full set of conjectures of Kudla, in turn, would give a conceptual proof and far-reaching generalizations of the work of Gross and Zagier on the Birch and Swinnerton-Dyer conjecture. Titles in this series are co-published with the Centre de Recherches Mathématiques.

Random Matrices and Their Applications

Joel E. Cohen,Harry Kesten,Charles Michael Newman
Random Matrices and Their Applications Book PDF

Author : Joel E. Cohen,Harry Kesten,Charles Michael Newman
Publisher : American Mathematical Soc.
Page : 376 pages
File Size : 41,5 Mb
Release : 1986
Category : Mathematics
ISBN : 9780821850442

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Random Matrices and Their Applications by Joel E. Cohen,Harry Kesten,Charles Michael Newman Pdf

Features twenty-six expository papers on random matrices and products of random matrices. This work reflects both theoretical and applied concerns in fields as diverse as computer science, probability theory, mathematical physics, and population biology.

Continuous Symmetries and Integrability of Discrete Equations

Decio Levi,Pavel Winternitz,Ravil I. Yamilov
Continuous Symmetries and Integrability of Discrete Equations Book PDF

Author : Decio Levi,Pavel Winternitz,Ravil I. Yamilov
Publisher : American Mathematical Society, Centre de Recherches Mathématiques
Page : 520 pages
File Size : 48,5 Mb
Release : 2023-01-23
Category : Mathematics
ISBN : 9780821843543

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Continuous Symmetries and Integrability of Discrete Equations by Decio Levi,Pavel Winternitz,Ravil I. Yamilov Pdf

This book on integrable systems and symmetries presents new results on applications of symmetries and integrability techniques to the case of equations defined on the lattice. This relatively new field has many applications, for example, in describing the evolution of crystals and molecular systems defined on lattices, and in finding numerical approximations for differential equations preserving their symmetries. The book contains three chapters and five appendices. The first chapter is an introduction to the general ideas about symmetries, lattices, differential difference and partial difference equations and Lie point symmetries defined on them. Chapter 2 deals with integrable and linearizable systems in two dimensions. The authors start from the prototype of integrable and linearizable partial differential equations, the Korteweg de Vries and the Burgers equations. Then they consider the best known integrable differential difference and partial difference equations. Chapter 3 considers generalized symmetries and conserved densities as integrability criteria. The appendices provide details which may help the readers' understanding of the subjects presented in Chapters 2 and 3. This book is written for PhD students and early researchers, both in theoretical physics and in applied mathematics, who are interested in the study of symmetries and integrability of difference equations.

Asymptotic Expansion of a Partition Function Related to the Sinh-model

Gaëtan Borot,Alice Guionnet,Karol K. Kozlowski
Asymptotic Expansion of a Partition Function Related to the Sinh model Book PDF

Author : Gaëtan Borot,Alice Guionnet,Karol K. Kozlowski
Publisher : Springer
Page : 222 pages
File Size : 50,9 Mb
Release : 2016-12-08
Category : Science
ISBN : 9783319333793

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Asymptotic Expansion of a Partition Function Related to the Sinh-model by Gaëtan Borot,Alice Guionnet,Karol K. Kozlowski Pdf

This book elaborates on the asymptotic behaviour, when N is large, of certain N-dimensional integrals which typically occur in random matrices, or in 1+1 dimensional quantum integrable models solvable by the quantum separation of variables. The introduction presents the underpinning motivations for this problem, a historical overview, and a summary of the strategy, which is applicable in greater generality. The core aims at proving an expansion up to o(1) for the logarithm of the partition function of the sinh-model. This is achieved by a combination of potential theory and large deviation theory so as to grasp the leading asymptotics described by an equilibrium measure, the Riemann-Hilbert approach to truncated Wiener-Hopf in order to analyse the equilibrium measure, the Schwinger-Dyson equations and the boostrap method to finally obtain an expansion of correlation functions and the one of the partition function. This book is addressed to researchers working in random matrices, statistical physics or integrable systems, or interested in recent developments of asymptotic analysis in those fields.