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El. knyga: Topics in Random Matrix Theory

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The field of random matrix theory has seen an explosion of activity in recent years, with connections to many areas of mathematics and physics. However, this makes the current state of the field almost too large to survey in a single book. In this graduate text, we focus on one specific sector of the field, namely the spectral distribution of random Wigner matrix ensembles (such as the Gaussian Unitary Ensemble), as well as iid matrix ensembles. The text is largely self-contained and starts with a review of relevant aspects of probability theory and linear algebra. With over 200 exercises, the book is suitable as an introductory text for beginning graduate students seeking to enter the field.

Recenzijos

This is a well-written book, providing a very accessible introduction for those with a solid background in probability and analysis. It is a terrific introduction to the subject, as the author constantly emphasizes where the various techniques can and cannot be used, and why. The author has succeeded in providing a good tour through an important part of random matrix theory, and readers will be well-prepared to continue further after reading this book. - Mathematical Reviews

The text is well-written and contains a large number of exercises, many of which are crucial for the main text. It will provide a good starting point for everybody interested in this area who has a solid background in measure theory and probability. - Springer

Preparatory material
Random matrices
Related articles
Bibliography
Index
Terence Tao, University of California, Los Angeles, CA.
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