An Introduction to Random Matrices
Seiten
2009
Cambridge University Press (Verlag)
978-0-521-19452-5 (ISBN)
Cambridge University Press (Verlag)
978-0-521-19452-5 (ISBN)
The theory of random matrices plays an important role in many areas of pure mathematics. This rigorous introduction is specifically designed for graduate students in mathematics or related sciences, who have a background in probability theory but have not been exposed to advanced notions of functional analysis, algebra or geometry.
The theory of random matrices plays an important role in many areas of pure mathematics and employs a variety of sophisticated mathematical tools (analytical, probabilistic and combinatorial). This diverse array of tools, while attesting to the vitality of the field, presents several formidable obstacles to the newcomer, and even the expert probabilist. This rigorous introduction to the basic theory is sufficiently self-contained to be accessible to graduate students in mathematics or related sciences, who have mastered probability theory at the graduate level, but have not necessarily been exposed to advanced notions of functional analysis, algebra or geometry. Useful background material is collected in the appendices and exercises are also included throughout to test the reader's understanding. Enumerative techniques, stochastic analysis, large deviations, concentration inequalities, disintegration and Lie algebras all are introduced in the text, which will enable readers to approach the research literature with confidence.
The theory of random matrices plays an important role in many areas of pure mathematics and employs a variety of sophisticated mathematical tools (analytical, probabilistic and combinatorial). This diverse array of tools, while attesting to the vitality of the field, presents several formidable obstacles to the newcomer, and even the expert probabilist. This rigorous introduction to the basic theory is sufficiently self-contained to be accessible to graduate students in mathematics or related sciences, who have mastered probability theory at the graduate level, but have not necessarily been exposed to advanced notions of functional analysis, algebra or geometry. Useful background material is collected in the appendices and exercises are also included throughout to test the reader's understanding. Enumerative techniques, stochastic analysis, large deviations, concentration inequalities, disintegration and Lie algebras all are introduced in the text, which will enable readers to approach the research literature with confidence.
Greg W. Anderson is Professor in the School of Mathematics at the University of Minnesota. Alice Guionnet is Director of Research at the Ecole Normale Supérieure in Lyon and the Centre National de la Recherche Scientifique (CNRS). Ofer Zeitouni is Professor of Mathematics at both the University of Minnesota and the Weizmann Institute of Science, Israel.
Preface; 1. Introduction; 2. Real and complex Wigner matrices; 3. Hermite polynomials, spacings, and limit distributions for the Gaussian ensembles; 4. Some generalities; 5. Free probability; Appendices; Bibliography; General conventions; Glossary; Index.
| Erscheint lt. Verlag | 19.11.2009 |
|---|---|
| Reihe/Serie | Cambridge Studies in Advanced Mathematics |
| Zusatzinfo | Worked examples or Exercises; 7 Line drawings, unspecified |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 155 x 229 mm |
| Gewicht | 840 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Analysis | |
| ISBN-10 | 0-521-19452-0 / 0521194520 |
| ISBN-13 | 978-0-521-19452-5 / 9780521194525 |
| Zustand | Neuware |
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