Random Matrices Frobenius Eigenvalues And Monodromy

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Random Matrices, Frobenius Eigenvalues, and Monodromy

Nicholas M. Katz,Peter Sarnak
Random Matrices Frobenius Eigenvalues and Monodromy Book PDF

Author : Nicholas M. Katz,Peter Sarnak
Publisher : American Mathematical Soc.
Page : 441 pages
File Size : 47,9 Mb
Release : 1999
Category : Fonctions L
ISBN : 9780821810170

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Random Matrices, Frobenius Eigenvalues, and Monodromy by Nicholas M. Katz,Peter Sarnak Pdf

The main topic of this book is the deep relation between the spacings between zeros of zeta and L-functions and spacings between eigenvalues of random elements of large compact classical groups. This relation, the Montgomery-Odlyzko law, is shown to hold for wide classes of zeta and L-functions over finite fields. The book draws on and gives accessible accounts of many disparate areas of mathematics, from algebraic geometry, moduli spaces, monodromy, equidistribution, and the Weil conjectures, to probability theory on the compact classical groups in the limit as their dimension goes to infinity and related techniques from orthogonal polynomials and Fredholm determinants.

Random Matrices, Frobenius Eigenvalues, and Monodromy

Nicholas M. Katz,Peter Sarnak
Random Matrices Frobenius Eigenvalues and Monodromy Book PDF

Author : Nicholas M. Katz,Peter Sarnak
Publisher : American Mathematical Society
Page : 441 pages
File Size : 51,8 Mb
Release : 2023-11-13
Category : Mathematics
ISBN : 9781470475079

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Random Matrices, Frobenius Eigenvalues, and Monodromy by Nicholas M. Katz,Peter Sarnak Pdf

The main topic of this book is the deep relation between the spacings between zeros of zeta and $L$-functions and spacings between eigenvalues of random elements of large compact classical groups. This relation, the Montgomery-Odlyzko law, is shown to hold for wide classes of zeta and $L$-functions over finite fields. The book draws on and gives accessible accounts of many disparate areas of mathematics, from algebraic geometry, moduli spaces, monodromy, equidistribution, and the Weil conjectures, to probability theory on the compact classical groups in the limit as their dimension goes to infinity and related techniques from orthogonal polynomials and Fredholm determinants.

Eigenvalue Distribution of Large Random Matrices

Leonid Andreevich Pastur,Mariya Shcherbina
Eigenvalue Distribution of Large Random Matrices Book PDF

Author : Leonid Andreevich Pastur,Mariya Shcherbina
Publisher : American Mathematical Soc.
Page : 650 pages
File Size : 55,7 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821852859

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Eigenvalue Distribution of Large Random Matrices by Leonid Andreevich Pastur,Mariya Shcherbina Pdf

Random matrix theory is a wide and growing field with a variety of concepts, results, and techniques and a vast range of applications in mathematics and the related sciences. The book, written by well-known experts, offers beginners a fairly balanced collection of basic facts and methods (Part 1 on classical ensembles) and presents experts with an exposition of recent advances in the subject (Parts 2 and 3 on invariant ensembles and ensembles with independent entries). The text includes many of the authors' results and methods on several main aspects of the theory, thus allowing them to present a unique and personal perspective on the subject and to cover many topics using a unified approach essentially based on the Stieltjes transform and orthogonal polynomials. The exposition is supplemented by numerous comments, remarks, and problems. This results in a book that presents a detailed and self-contained treatment of the basic random matrix ensembles and asymptotic regimes. This book will be an important reference for researchers in a variety of areas of mathematics and mathematical physics. Various chapters of the book can be used for graduate courses; the main prerequisite is a basic knowledge of calculus, linear algebra, and probability theory.

Mathematical Constants

Steven R. Finch
Mathematical Constants Book PDF

Author : Steven R. Finch
Publisher : Cambridge University Press
Page : 634 pages
File Size : 47,5 Mb
Release : 2003-08-18
Category : Mathematics
ISBN : 0521818052

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Mathematical Constants by Steven R. Finch Pdf

Steven Finch provides 136 essays, each devoted to a mathematical constant or a class of constants, from the well known to the highly exotic. This book is helpful both to readers seeking information about a specific constant, and to readers who desire a panoramic view of all constants coming from a particular field, for example, combinatorial enumeration or geometric optimization. Unsolved problems appear virtually everywhere as well. This work represents an outstanding scholarly attempt to bring together all significant mathematical constants in one place.

Random Matrices and Iterated Random Functions

Gerold Alsmeyer,Matthias Löwe
Random Matrices and Iterated Random Functions Book PDF

Author : Gerold Alsmeyer,Matthias Löwe
Publisher : Springer Science & Business Media
Page : 265 pages
File Size : 45,5 Mb
Release : 2013-08-28
Category : Mathematics
ISBN : 9783642388064

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Random Matrices and Iterated Random Functions by Gerold Alsmeyer,Matthias Löwe Pdf

​Random Matrices are one of the major research areas in modern probability theory, due to their prominence in many different fields such as nuclear physics, statistics, telecommunication, free probability, non-commutative geometry, and dynamical systems. A great deal of recent work has focused on the study of spectra of large random matrices on the one hand and on iterated random functions, especially random difference equations, on the other. However, the methods applied in these two research areas are fairly dissimilar. Motivated by the idea that tools from one area could potentially also be helpful in the other, the volume editors have selected contributions that present results and methods from random matrix theory as well as from the theory of iterated random functions. This work resulted from a workshop that was held in Münster, Germany in 2011. The aim of the workshop was to bring together researchers from two fields of probability theory: random matrix theory and the theory of iterated random functions. Random matrices play fundamental, yet very different roles in the two fields. Accordingly, leading figures and young researchers gave talks on their field of interest that were also accessible to a broad audience.

Embedded Random Matrix Ensembles in Quantum Physics

V.K.B. Kota
Embedded Random Matrix Ensembles in Quantum Physics Book PDF

Author : V.K.B. Kota
Publisher : Springer
Page : 401 pages
File Size : 45,7 Mb
Release : 2014-07-08
Category : Science
ISBN : 9783319045672

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Embedded Random Matrix Ensembles in Quantum Physics by V.K.B. Kota Pdf

Although used with increasing frequency in many branches of physics, random matrix ensembles are not always sufficiently specific to account for important features of the physical system at hand. One refinement which retains the basic stochastic approach but allows for such features consists in the use of embedded ensembles. The present text is an exhaustive introduction to and survey of this important field. Starting with an easy-to-read introduction to general random matrix theory, the text then develops the necessary concepts from the beginning, accompanying the reader to the frontiers of present-day research. With some notable exceptions, to date these ensembles have primarily been applied in nuclear spectroscopy. A characteristic example is the use of a random two-body interaction in the framework of the nuclear shell model. Yet, topics in atomic physics, mesoscopic physics, quantum information science and statistical mechanics of isolated finite quantum systems can also be addressed using these ensembles. This book addresses graduate students and researchers with an interest in applications of random matrix theory to the modeling of more complex physical systems and interactions, with applications such as statistical spectroscopy in mind.

Integrable Systems and Random Matrices

Jinho Baik,T. Kriecherbauer,Luen-Chau Li,Kenneth D. T-R McLaughlin,Carlos Tomei
Integrable Systems and Random Matrices Book PDF

Author : Jinho Baik,T. Kriecherbauer,Luen-Chau Li,Kenneth D. T-R McLaughlin,Carlos Tomei
Publisher : American Mathematical Soc.
Page : 448 pages
File Size : 47,7 Mb
Release : 2008
Category : Hamiltonian systems
ISBN : 9780821842409

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Integrable Systems and Random Matrices by Jinho Baik,T. Kriecherbauer,Luen-Chau Li,Kenneth D. T-R McLaughlin,Carlos Tomei 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.

Random Matrix Theory

Percy Deift,Dimitri Gioev
Random Matrix Theory Book PDF

Author : Percy Deift,Dimitri Gioev
Publisher : American Mathematical Soc.
Page : 236 pages
File Size : 52,6 Mb
Release : 2009-01-01
Category : Mathematics
ISBN : 9780821883570

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Random Matrix Theory by Percy Deift,Dimitri Gioev Pdf

"This book features a unified derivation of the mathematical theory of the three classical types of invariant random matrix ensembles-orthogonal, unitary, and symplectic. The authors follow the approach of Tracy and Widom, but the exposition here contains a substantial amount of additional material, in particular, facts from functional analysis and the theory of Pfaffians. The main result in the book is a proof of universality for orthogonal and symplectic ensembles corresponding to generalized Gaussian type weights following the authors' prior work. New, quantitative error estimates are derived." --Book Jacket.

Log-Gases and Random Matrices (LMS-34)

Peter J. Forrester
Log Gases and Random Matrices LMS 34 Book PDF

Author : Peter J. Forrester
Publisher : Princeton University Press
Page : 808 pages
File Size : 41,5 Mb
Release : 2010-07-01
Category : Mathematics
ISBN : 9781400835416

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Log-Gases and Random Matrices (LMS-34) by Peter J. Forrester Pdf

Random matrix theory, both as an application and as a theory, has evolved rapidly over the past fifteen years. Log-Gases and Random Matrices gives a comprehensive account of these developments, emphasizing log-gases as a physical picture and heuristic, as well as covering topics such as beta ensembles and Jack polynomials. Peter Forrester presents an encyclopedic development of log-gases and random matrices viewed as examples of integrable or exactly solvable systems. Forrester develops not only the application and theory of Gaussian and circular ensembles of classical random matrix theory, but also of the Laguerre and Jacobi ensembles, and their beta extensions. Prominence is given to the computation of a multitude of Jacobians; determinantal point processes and orthogonal polynomials of one variable; the Selberg integral, Jack polynomials, and generalized hypergeometric functions; Painlevé transcendents; macroscopic electrostatistics and asymptotic formulas; nonintersecting paths and models in statistical mechanics; and applications of random matrix theory. This is the first textbook development of both nonsymmetric and symmetric Jack polynomial theory, as well as the connection between Selberg integral theory and beta ensembles. The author provides hundreds of guided exercises and linked topics, making Log-Gases and Random Matrices an indispensable reference work, as well as a learning resource for all students and researchers in the field.

Ranks of Elliptic Curves and Random Matrix Theory

J. B. Conrey
Ranks of Elliptic Curves and Random Matrix Theory Book PDF

Author : J. B. Conrey
Publisher : Cambridge University Press
Page : 5 pages
File Size : 41,7 Mb
Release : 2007-02-08
Category : Mathematics
ISBN : 9780521699648

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Ranks of Elliptic Curves and Random Matrix Theory by J. B. Conrey Pdf

This comprehensive volume introduces elliptic curves and the fundamentals of modeling by a family of random matrices.

The Random Matrix Theory of the Classical Compact Groups

Elizabeth S. Meckes
The Random Matrix Theory of the Classical Compact Groups Book PDF

Author : Elizabeth S. Meckes
Publisher : Cambridge University Press
Page : 225 pages
File Size : 47,8 Mb
Release : 2019-08
Category : Mathematics
ISBN : 9781108419529

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The Random Matrix Theory of the Classical Compact Groups by Elizabeth S. Meckes Pdf

Provides a comprehensive introduction to the theory of random orthogonal, unitary, and symplectic matrices.

Applications of Random Matrices in Physics

Édouard Brezin,Vladimir Kazakov,Didina Serban,Paul Wiegmann,Anton Zabrodin
Applications of Random Matrices in Physics Book PDF

Author : Édouard Brezin,Vladimir Kazakov,Didina Serban,Paul Wiegmann,Anton Zabrodin
Publisher : Springer Science & Business Media
Page : 519 pages
File Size : 49,5 Mb
Release : 2006-07-03
Category : Science
ISBN : 9781402045318

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Applications of Random Matrices in Physics by Édouard Brezin,Vladimir Kazakov,Didina Serban,Paul Wiegmann,Anton Zabrodin Pdf

Random matrices are widely and successfully used in physics for almost 60-70 years, beginning with the works of Dyson and Wigner. Although it is an old subject, it is constantly developing into new areas of physics and mathematics. It constitutes now a part of the general culture of a theoretical physicist. Mathematical methods inspired by random matrix theory become more powerful, sophisticated and enjoy rapidly growing applications in physics. Recent examples include the calculation of universal correlations in the mesoscopic system, new applications in disordered and quantum chaotic systems, in combinatorial and growth models, as well as the recent breakthrough, due to the matrix models, in two dimensional gravity and string theory and the non-abelian gauge theories. The book consists of the lectures of the leading specialists and covers rather systematically many of these topics. It can be useful to the specialists in various subjects using random matrices, from PhD students to confirmed scientists.

Stochastic Processes and Random Matrices

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

Author : Grégory Schehr,Alexander Altland,Yan V. Fyodorov,Neil O'Connell,Leticia F. Cugliandolo
Publisher : Oxford University Press
Page : 432 pages
File Size : 43,6 Mb
Release : 2017-08-15
Category : Science
ISBN : 9780192517869

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

The field of stochastic processes and Random Matrix Theory (RMT) has been a rapidly evolving subject during the last fifteen years. The continuous development and discovery of new tools, connections and ideas have led to an avalanche of new results. These breakthroughs have been made possible thanks, to a large extent, to the recent development of various new techniques in RMT. Matrix models have been playing an important role in theoretical physics for a long time and they are currently also a very active domain of research in mathematics. An emblematic example of these recent advances concerns the theory of growth phenomena in the Kardar-Parisi-Zhang (KPZ) universality class where the joint efforts of physicists and mathematicians during the last twenty years have unveiled the beautiful connections between this fundamental problem of statistical mechanics and the theory of random matrices, namely the fluctuations of the largest eigenvalue of certain ensembles of random matrices. This text not only covers this topic in detail but also presents more recent developments that have emerged from these discoveries, for instance in the context of low dimensional heat transport (on the physics side) or integrable probability (on the mathematical side).

Recent Perspectives in Random Matrix Theory and Number Theory

F. Mezzadri,N. C. Snaith
Recent Perspectives in Random Matrix Theory and Number Theory Book PDF

Author : F. Mezzadri,N. C. Snaith
Publisher : Cambridge University Press
Page : 530 pages
File Size : 42,9 Mb
Release : 2005-06-21
Category : Mathematics
ISBN : 9780521620581

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Recent Perspectives in Random Matrix Theory and Number Theory by F. Mezzadri,N. C. Snaith Pdf

Provides a grounding in random matrix techniques applied to analytic number theory.

Random Matrices

Madan Lal Mehta
Random Matrices Book PDF

Author : Madan Lal Mehta
Publisher : Elsevier
Page : 707 pages
File Size : 43,8 Mb
Release : 2004-10-06
Category : Mathematics
ISBN : 9780080474113

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Random Matrices by Madan Lal Mehta Pdf

Random Matrices gives a coherent and detailed description of analytical methods devised to study random matrices. These methods are critical to the understanding of various fields in in mathematics and mathematical physics, such as nuclear excitations, ultrasonic resonances of structural materials, chaotic systems, the zeros of the Riemann and other zeta functions. More generally they apply to the characteristic energies of any sufficiently complicated system and which have found, since the publication of the second edition, many new applications in active research areas such as quantum gravity, traffic and communications networks or stock movement in the financial markets. This revised and enlarged third edition reflects the latest developements in the field and convey a greater experience with results previously formulated. For example, the theory of skew-orthogoanl and bi-orthogonal polynomials, parallel to that of the widely known and used orthogonal polynomials, is explained here for the first time. Presentation of many new results in one place for the first time First time coverage of skew-orthogonal and bi-orthogonal polynomials and their use in the evaluation of some multiple integrals Fredholm determinants and Painlevé equations The three Gaussian ensembles (unitary, orthogonal, and symplectic); their n-point correlations, spacing probabilities Fredholm determinants and inverse scattering theory Probability densities of random determinants