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Author : Elizabeth S. Meckes
Publisher : Cambridge University Press
Page : 225 pages
File Size : 41,7 Mb
Release : 2019-08
Category : Mathematics
ISBN : 9781108419529
Provides a comprehensive introduction to the theory of random orthogonal, unitary, and symplectic matrices.
Author : F. Mezzadri,N. C. Snaith
Publisher : Cambridge University Press
Page : 530 pages
File Size : 46,9 Mb
Release : 2005-06-21
Category : Mathematics
ISBN : 9780521620581
Provides a grounding in random matrix techniques applied to analytic number theory.
Author : Nicholas M. Katz,Peter Sarnak
Publisher : American Mathematical Soc.
Page : 441 pages
File Size : 49,8 Mb
Release : 1999
Category : Fonctions L
ISBN : 9780821810170
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.
Author : Giacomo Livan,Marcel Novaes,Pierpaolo Vivo
Publisher : Springer
Page : 124 pages
File Size : 44,5 Mb
Release : 2018-01-16
Category : Science
ISBN : 9783319708850
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.
Author : Leonid Andreevich Pastur,Mariya Shcherbina
Publisher : American Mathematical Soc.
Page : 650 pages
File Size : 42,5 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821852859
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.
Author : Greg W. Anderson,Alice Guionnet,Ofer Zeitouni
Publisher : Cambridge University Press
Page : 507 pages
File Size : 47,6 Mb
Release : 2010
Category : Mathematics
ISBN : 9780521194525
A rigorous introduction to the basic theory of random matrices designed for graduate students with a background in probability theory.
Author : James A. Mingo,Roland Speicher
Publisher : Springer
Page : 336 pages
File Size : 43,7 Mb
Release : 2017-06-24
Category : Mathematics
ISBN : 9781493969425
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.
Author : Carl Pomerance,Michael Th. Rassias
Publisher : Springer
Page : 379 pages
File Size : 48,5 Mb
Release : 2015-11-18
Category : Mathematics
ISBN : 9783319222400
This volume contains a collection of research and survey papers written by some of the most eminent mathematicians in the international community and is dedicated to Helmut Maier, whose own research has been groundbreaking and deeply influential to the field. Specific emphasis is given to topics regarding exponential and trigonometric sums and their behavior in short intervals, anatomy of integers and cyclotomic polynomials, small gaps in sequences of sifted prime numbers, oscillation theorems for primes in arithmetic progressions, inequalities related to the distribution of primes in short intervals, the Möbius function, Euler’s totient function, the Riemann zeta function and the Riemann Hypothesis. Graduate students, research mathematicians, as well as computer scientists and engineers who are interested in pure and interdisciplinary research, will find this volume a useful resource. Contributors to this volume: Bill Allombert, Levent Alpoge, Nadine Amersi, Yuri Bilu, Régis de la Bretèche, Christian Elsholtz, John B. Friedlander, Kevin Ford, Daniel A. Goldston, Steven M. Gonek, Andrew Granville, Adam J. Harper, Glyn Harman, D. R. Heath-Brown, Aleksandar Ivić, Geoffrey Iyer, Jerzy Kaczorowski, Daniel M. Kane, Sergei Konyagin, Dimitris Koukoulopoulos, Michel L. Lapidus, Oleg Lazarev, Andrew H. Ledoan, Robert J. Lemke Oliver, Florian Luca, James Maynard, Steven J. Miller, Hugh L. Montgomery, Melvyn B. Nathanson, Ashkan Nikeghbali, Alberto Perelli, Amalia Pizarro-Madariaga, János Pintz, Paul Pollack, Carl Pomerance, Michael Th. Rassias, Maksym Radziwiłł, Joël Rivat, András Sárközy, Jeffrey Shallit, Terence Tao, Gérald Tenenbaum, László Tóth, Tamar Ziegler, Liyang Zhang.
Author : J. B. Conrey
Publisher : Cambridge University Press
Page : 5 pages
File Size : 54,7 Mb
Release : 2007-02-08
Category : Mathematics
ISBN : 9780521699648
This comprehensive volume introduces elliptic curves and the fundamentals of modeling by a family of random matrices.
Author : Christian Rosendal
Publisher : Cambridge University Press
Page : 309 pages
File Size : 41,7 Mb
Release : 2021-12-16
Category : Mathematics
ISBN : 9781108842471
Provides a general framework for doing geometric group theory for non-locally-compact topological groups arising in mathematical practice.
Author : László Erdős,Horng-Tzer Yau
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 47,5 Mb
Release : 2017-08-30
Category : Random matrices
ISBN : 9781470436483
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 : Joseph A. Ball,Vladimir Bolotnikov
Publisher : Cambridge University Press
Page : 439 pages
File Size : 55,7 Mb
Release : 2021-12-16
Category : Mathematics
ISBN : 9781316518991
This concise volume shows how ideas from function and systems theory lead to new insights for noncommutative multivariable operator theory.
Author : Hideaki Ikoma,Shu Kawaguchi,Atsushi Moriwaki
Publisher : Cambridge University Press
Page : 179 pages
File Size : 52,7 Mb
Release : 2022-02-03
Category : Mathematics
ISBN : 9781108845953
This book provides a self-contained proof of the Mordell conjecture (Faltings's theorem) and a concise introduction to Diophantine geometry.
Author : Alexander Komech,Elena Kopylova
Publisher : Cambridge University Press
Page : 128 pages
File Size : 50,9 Mb
Release : 2021-09-30
Category : Mathematics
ISBN : 9781009036054
This monograph is the first to present the theory of global attractors of Hamiltonian partial differential equations. A particular focus is placed on the results obtained in the last three decades, with chapters on the global attraction to stationary states, to solitons, and to stationary orbits. The text includes many physically relevant examples and will be of interest to graduate students and researchers in both mathematics and physics. The proofs involve novel applications of methods of harmonic analysis, including Tauberian theorems, Titchmarsh's convolution theorem, and the theory of quasimeasures. As well as the underlying theory, the authors discuss the results of numerical simulations and formulate open problems to prompt further research.
Author : Jonathan Pila
Publisher : Cambridge University Press
Page : 267 pages
File Size : 49,6 Mb
Release : 2022-06-09
Category : Mathematics
ISBN : 9781009170321
Explores the recent spectacular applications of point-counting in o-minimal structures to functional transcendence and diophantine geometry.