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.
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.
Volume 2 offers three in-depth articles covering significant areas in applied mathematics research. Chapters feature numerous illustrations, extensive background material and technical details, and abundant examples. The authors analyze nonlinear front propagation for a large class of semilinear partial differential equations using probabilistic methods; examine wave localization phenomena in one-dimensional random media; and offer an extensive introduction to certain model equations for nonlinear wave phenomena.
Volume 2 offers three in-depth articles covering significant areas in applied mathematics research. Chapters feature numerous illustrations, extensive background material and technical details, and abundant examples. The authors analyze nonlinear front propagation for a large class of semilinear partial differential equations using probabilistic methods; examine wave localization phenomena in one-dimensional random media; and offer an extensive introduction to certain model equations for nonlinear wave phenomena.
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.
Asymptotic methods belong to the, perhaps, most romantic area of modern mathematics. They are widely known and have been used in me chanics, physics and other exact sciences for many, many decades. But more than this, asymptotic ideas are found in all branches of human knowledge, indeed in all areas of life. In this broader context they have not and perhaps cannot be fully formalized. However, they are mar velous, they leave room for fantasy, guesses and intuition; they bring us very near to the border of the realm of art. Many books have been written and published about asymptotic meth ods. Most of them presume a mathematically sophisticated reader. The authors here attempt to describe asymptotic methods on a more accessi ble level, hoping to address a wider range of readers. They have avoided the extreme of banishing formulae entirely, as done in some popular science books that attempt to describe mathematical methods with no mathematics. This is impossible (and not wise). Rather, the authors have tried to keep the mathematics at a moderate level. At the same time, using simple examples, they think they have been able to illustrate all the key ideas of asymptotic methods and approaches, to depict in de tail the results of their application to various branches of knowledg- from astronomy, mechanics, and physics to biology, psychology and art. The book is supplemented by several appendices, one of which con tains the profound ideas of R. G.
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