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Mathematical Surveys and Monographs
2011; 632 pp; hardcover
List Price: US$105
Member Price: US$84
Order Code: SURV/171
Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach - Percy Deift
Random Matrix Theory: Invariant Ensembles and Universality - Percy Deift and Dimitri Gioev
Random Matrices, Frobenius Eigenvalues, and Monodromy - Nicholas M Katz and Peter Sarnak
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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