Eigenvalue Distribution of Large Random Matrices (Mathematical Surveys and Monographs) (Mathematical Surveys and Monographs, 171)

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 This Introduction To Modern Methods Of The Theory Of Random Matrices Includes Both Basic Facts And Expert-oriented Recent Advances. Inclusion Of Many Of The Authors' Results On Main Aspects Of The Theory Provides A Unified Approach Essentially Based On The Stieltjes Transform And Orthogonal Polynomials. Many Of The New Developments Are Presented For The First Time In Book Form. 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. This Book Offers Beginners A Fairly Balanced Collection Of Basic Facts And Methods. Leonid Pastur, Mariya Shcherbina. Includes Bibliographical References (p. 611-629) And Index.