The preface explains that the study of random matrixes was "[i]nitiated in the 1920s-1930s by statisticians and introduced in physics in the 1950s-1960s...[it] has become very active since the end of the 1970s under the flow of accelerating impulses from quantum field theory, quantum mechanics..., statistical mechanics, and condensed matter theory in physics, probability theory, statistics, combinatorics, operator theory, number theory, and theoretical computer science in mathematics, and also telecommunications theory, qualitative finances, structural mechanics, etc." The authors (whose affiliations are not stated) explain the scope of the field and the book's arrangement in three parts: the first devoted to classical ensembles, the second to the matrix models, and the third to "ensembles determined by independent but not necessarily Gaussian random variables." Annotation ©2011 Book News, Inc., Portland, OR (booknews.com)
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Leonid Pastur, Ukrainian National Academy of Sciences, Kharkov, Ukraine||Mariya Shcherbina, Ukrainian National Academy of Sciences, Kharkov, Ukrain
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Hardback. Zustand: New. 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. Artikel-Nr. LU-9780821852859
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