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Eigenvalue Distribution of Large Random Matrices
Leonid Pastur and Mariya Shcherbina, Ukrainian National Academy of Sciences, Kharkov, Ukraine

Mathematical Surveys and Monographs
2011; 632 pp; hardcover
Volume: 171
ISBN-10: 0-8218-5285-X
ISBN-13: 978-0-8218-5285-9
List Price: US$110
Member Price: US$88
Order Code: SURV/171
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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.


Graduate students and research mathematicians interested in random matrix theory and its applications.


"While a wide variety of ensembles are studied in this text, the methods are coherently focused, relying heavily in particular on Stieltjes transform based tools. This gives a slightly different perspective on the subject from other recent texts which often focus on other methods."

-- Mathematical Reviews

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