
Contents
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Abstract Abstract
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1.1 Random matrix theory in a nutshell 1.1 Random matrix theory in a nutshell
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1.2 What is random matrix theory about? 1.2 What is random matrix theory about?
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1.3 Why is random matrix theory so successful in applications? 1.3 Why is random matrix theory so successful in applications?
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1.4 Guide to this handbook 1.4 Guide to this handbook
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1.5 What is not covered in detail 1.5 What is not covered in detail
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1.6 Some existing introductory literature 1.6 Some existing introductory literature
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Acknowledgements Acknowledgements
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References References
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·1· Introduction and guide to the handbook
Get accessGernot Akemann, Fakultät für Physik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany, [email protected]
Jinho Baik, 530 Church Street, Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1043, USA, [email protected]
Philippe Di Francesco, Institut de Physique Théorique, CEA/Saclay, Orme des Merisiers, F-91191 Gif-sur-Yvette Cedex, France, [email protected]
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Published:08 August 2018
Cite
Abstract
This article discusses random matrix theory (RMT) in a nutshell — what it is about, what its main features are, and why it is so successful in applications. It first considers the simplest and maybe most frequently used standard example, the Gaussian Unitary Ensemble (GUE) of random matrices, before looking at several types of applications of RMT, focusing on random operators, counting devices, and RMT without matrices. It then provides a guide to the handbook, explaining how the other forty-two articles on mathematical properties and applications of random matrices are related and built one upon the other. It also lists some topics that are not covered in detail in the book and reviews recent new developments since the first edition of this handbook before concluding with a brief survey of the existing introductory literature.
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