Download Full eBooks in PDF
Recent Perspectives In Random Matrix Theory And Number Theory Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Recent Perspectives In Random Matrix Theory And Number Theory book. This book definitely worth reading, it is an incredibly well-written.
Author : F. Mezzadri,N. C. Snaith
Publisher : Cambridge University Press
Page : 530 pages
File Size : 52,5 Mb
Release : 2005-06-21
Category : Mathematics
ISBN : 9780521620581
Provides a grounding in random matrix techniques applied to analytic number theory.
Author : Steven J. Miller,Ramin Takloo-Bighash
Publisher : Princeton University Press
Page : 128 pages
File Size : 40,9 Mb
Release : 2020-08-04
Category : Mathematics
ISBN : 9780691215976
In a manner accessible to beginning undergraduates, An Invitation to Modern Number Theory introduces many of the central problems, conjectures, results, and techniques of the field, such as the Riemann Hypothesis, Roth's Theorem, the Circle Method, and Random Matrix Theory. Showing how experiments are used to test conjectures and prove theorems, the book allows students to do original work on such problems, often using little more than calculus (though there are numerous remarks for those with deeper backgrounds). It shows students what number theory theorems are used for and what led to them and suggests problems for further research. Steven Miller and Ramin Takloo-Bighash introduce the problems and the computational skills required to numerically investigate them, providing background material (from probability to statistics to Fourier analysis) whenever necessary. They guide students through a variety of problems, ranging from basic number theory, cryptography, and Goldbach's Problem, to the algebraic structures of numbers and continued fractions, showing connections between these subjects and encouraging students to study them further. In addition, this is the first undergraduate book to explore Random Matrix Theory, which has recently become a powerful tool for predicting answers in number theory. Providing exercises, references to the background literature, and Web links to previous student research projects, An Invitation to Modern Number Theory can be used to teach a research seminar or a lecture class.
Author : Alexei Borodin,Ivan Corwin,Alice Guionnet
Publisher : American Mathematical Soc.
Page : 498 pages
File Size : 50,6 Mb
Release : 2019-10-30
Category : Education
ISBN : 9781470452803
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 : Giacomo Livan,Marcel Novaes,Pierpaolo Vivo
Publisher : Springer
Page : 124 pages
File Size : 47,8 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 : 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 : Grégory Schehr,Alexander Altland,Yan V. Fyodorov,Neil O'Connell,Leticia F. Cugliandolo
Publisher : Oxford University Press
Page : 432 pages
File Size : 47,9 Mb
Release : 2017-08-15
Category : Science
ISBN : 9780192517869
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).
Author : Elizabeth S. Meckes
Publisher : Cambridge University Press
Page : 225 pages
File Size : 45,7 Mb
Release : 2019-08
Category : Mathematics
ISBN : 9781108419529
Provides a comprehensive introduction to the theory of random orthogonal, unitary, and symplectic matrices.
Author : Pavel Bleher,Alexander Its
Publisher : Cambridge University Press
Page : 454 pages
File Size : 50,5 Mb
Release : 2001-06-04
Category : Mathematics
ISBN : 0521802091
Expository articles on random matrix theory emphasizing the exchange of ideas between the physical and mathematical communities.
Author : László Erdős,Horng-Tzer Yau
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 44,8 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 : Greg W. Anderson,Alice Guionnet,Ofer Zeitouni
Publisher : Cambridge University Press
Page : 507 pages
File Size : 55,6 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 : Zhonggen Su
Publisher : World Scientific
Page : 284 pages
File Size : 49,6 Mb
Release : 2015-04-20
Category : Mathematics
ISBN : 9789814612241
This book is aimed at graduate students and researchers who are interested in the probability limit theory of random matrices and random partitions. It mainly consists of three parts. Part I is a brief review of classical central limit theorems for sums of independent random variables, martingale differences sequences and Markov chains, etc. These classical theorems are frequently used in the study of random matrices and random partitions. Part II concentrates on the asymptotic distribution theory of Circular Unitary Ensemble and Gaussian Unitary Ensemble, which are prototypes of random matrix theory. It turns out that the classical central limit theorems and methods are applicable in describing asymptotic distributions of various eigenvalue statistics. This is attributed to the nice algebraic structures of models. This part also studies the Circular β Ensembles and Hermitian β Ensembles. Part III is devoted to the study of random uniform and Plancherel partitions. There is a surprising similarity between random matrices and random integer partitions from the viewpoint of asymptotic distribution theory, though it is difficult to find any direct link between the two finite models. A remarkable point is the conditioning argument in each model. Through enlarging the probability space, we run into independent geometric random variables as well as determinantal point processes with discrete Bessel kernels.This book treats only second-order normal fluctuations for primary random variables from two classes of special random models. It is written in a clear, concise and pedagogical way. It may be read as an introductory text to further study probability theory of general random matrices, random partitions and even random point processes.
Author : Peter J. Forrester
Publisher : Princeton University Press
Page : 808 pages
File Size : 54,5 Mb
Release : 2010-07-01
Category : Mathematics
ISBN : 9781400835416
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.
Author : Dzmitry Badziahin,Alexander Gorodnik,Norbert Peyerimhoff
Publisher : Cambridge University Press
Page : 341 pages
File Size : 44,7 Mb
Release : 2016-11-10
Category : Mathematics
ISBN : 9781107552371
Presents current research in various topics, including homogeneous dynamics, Diophantine approximation and combinatorics.
Author : Arthur T. Benjamin,Ezra Brown
Publisher : American Mathematical Soc.
Page : 311 pages
File Size : 54,7 Mb
Release : 2020-07-29
Category : Mathematics
ISBN : 9781470458430
Author : Gordon Blower
Publisher : Cambridge University Press
Page : 448 pages
File Size : 44,5 Mb
Release : 2009-10-08
Category : Mathematics
ISBN : 9781139481953
This book focuses on the behaviour of large random matrices. Standard results are covered, and the presentation emphasizes elementary operator theory and differential equations, so as to be accessible to graduate students and other non-experts. The introductory chapters review material on Lie groups and probability measures in a style suitable for applications in random matrix theory. Later chapters use modern convexity theory to establish subtle results about the convergence of eigenvalue distributions as the size of the matrices increases. Random matrices are viewed as geometrical objects with large dimension. The book analyzes the concentration of measure phenomenon, which describes how measures behave on geometrical objects with large dimension. To prove such results for random matrices, the book develops the modern theory of optimal transportation and proves the associated functional inequalities involving entropy and information. These include the logarithmic Sobolev inequality, which measures how fast some physical systems converge to equilibrium.
