Book Library

Author: Terence Tao
Publisher: American Mathematical Soc.
ISBN: 0821874306
Size: 71.94 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 282
View: 6015

Book Description: The field of random matrix theory has seen an explosion of activity in recent years, with connections to many areas of mathematics and physics. However, this makes the current state of the field almost too large to survey in a single book. In this graduate text, we focus on one specific sector of the field, namely the spectral distribution of random Wigner matrix ensembles (such as the Gaussian Unitary Ensemble), as well as iid matrix ensembles. The text is largely self-contained and starts with a review of relevant aspects of probability theory and linear algebra. With over 200 exercises, the book is suitable as an introductory text for beginning graduate students seeking to enter the field.

Author: Termeh Kousha
Publisher:
ISBN:
Size: 12.98 MB
Format: PDF
Category :
Languages : en
Pages :
View: 1691

Book Description:

Author: Van H. Vu
Publisher: American Mathematical Society
ISBN: 0821894714
Size: 11.96 MB
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 176
View: 5740

Book Description: The theory of random matrices is an amazingly rich topic in mathematics. Random matrices play a fundamental role in various areas such as statistics, mathematical physics, combinatorics, theoretical computer science, number theory and numerical analysis. This volume is based on lectures delivered at the 2013 AMS Short Course on Random Matrices, held January 6-7, 2013 in San Diego, California. Included are surveys by leading researchers in the field, written in introductory style, aiming to provide the reader a quick and intuitive overview of this fascinating and rapidly developing topic. These surveys contain many major recent developments, such as progress on universality conjectures, connections between random matrices and free probability, numerical algebra, combinatorics and high-dimensional geometry, together with several novel methods and a variety of open questions.

Author: F. Mezzadri
Publisher: Cambridge University Press
ISBN: 9780521620581
Size: 39.37 MB
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages : 518
View: 3960

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

Author: Percy Deift
Publisher: Cambridge University Press
ISBN: 1107079926
Size: 75.91 MB
Format: PDF, Kindle
Category : Language Arts & Disciplines
Languages : en
Pages : 552
View: 2279

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

Author:
Publisher:
ISBN:
Size: 37.55 MB
Format: PDF, ePub
Category : Nuclear energy
Languages : en
Pages :
View: 4828

Book Description:

Author: Arunava Mukherjea
Publisher:
ISBN:
Size: 44.25 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages : 121
View: 2459

Book Description: These lecture notes contain detailed results on convergence in distribution for products of independent and identically distributed random matrices and also for their normalised versions. Conditions for the limit distribution to be absolutely continuous or continuous singular are discussed and the limit distributions have also been computed for various specific examples. Infinite dimensional matrices are also considered, with reference to random motions of particles. Semigroup methods have been highlighted throughout the notes. Care has been taken to make the presentation readily accessible to graduate students and beginners in research. Most of the results presented in the notes have not previously appeared in book form.

Author: Édouard Brezin
Publisher: Springer Science & Business Media
ISBN: 9781402045295
Size: 24.80 MB
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 513
View: 838

Book Description: Proceedings of the NATO Advanced Study Institute on Applications of Random Matrices in Physics, Les Houches, France, 6-25 June 2004

Author: Marc Potters
Publisher: Cambridge University Press
ISBN: 1108488080
Size: 74.90 MB
Format: PDF, ePub
Category : Computers
Languages : en
Pages : 370
View: 5555

Book Description: An intuitive, up-to-date introduction to random matrix theory and free calculus, with real world illustrations and Big Data applications.

Author: László Erdős
Publisher: American Mathematical Soc.
ISBN: 1470436485
Size: 18.85 MB
Format: PDF, ePub, Mobi
Category : Random matrices
Languages : en
Pages : 226
View: 6365

Book Description: 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: Alberto Bressan
Publisher: American Mathematical Soc.
ISBN: 0821887718
Size: 76.12 MB
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages : 250
View: 4934

Book Description: This textbook is addressed to graduate students in mathematics or other disciplines who wish to understand the essential concepts of functional analysis and their applications to partial differential equations. The book is intentionally concise, presenting all the fundamental concepts and results but omitting the more specialized topics. Enough of the theory of Sobolev spaces and semigroups of linear operators is included as needed to develop significant applications to elliptic, parabolic, and hyperbolic PDEs. Throughout the book, care has been taken to explain the connections between theorems in functional analysis and familiar results of finite-dimensional linear algebra. The main concepts and ideas used in the proofs are illustrated with a large number of figures. A rich collection of homework problems is included at the end of most chapters. The book is suitable as a text for a one-semester graduate course.

Author:
Publisher:
ISBN:
Size: 13.15 MB
Format: PDF
Category : Mathematics
Languages : ru
Pages :
View: 573

Book Description: