A dynamical approach to random matrix theory
Introduction -- Wigner matrices and their generalizations -- Eigenvalue density -- Invariant ensembles -- Universality for generalized Wigner matrices -- Local semicircle law for universal Wigner matrices -- Weak local semicircle law -- Proof of the local semicircle law -- Sketch of the proof of the...
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| Körperschaften: | , |
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| Format: | UnknownFormat |
| Sprache: | eng |
| Veröffentlicht: |
New York, New York
Courant Institute of Mathematical Sciences, New York University
2017
Providence, Rhode Island American Mathematical Society 2017 |
| Schriftenreihe: | Courant lecture notes in mathematics
28 |
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| Online Zugang: | Inhaltsverzeichnis Inhaltstext |
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Tag hinzufügen | Zusammenfassung: | Introduction -- Wigner matrices and their generalizations -- Eigenvalue density -- Invariant ensembles -- Universality for generalized Wigner matrices -- Local semicircle law for universal Wigner matrices -- Weak local semicircle law -- Proof of the local semicircle law -- Sketch of the proof of the local semicircle law -- Fluctuation averaging mechanism -- Eigenvalue location: the rigidity phenomenon -- Universality for matrices with Guassian convolutions -- Entropy and the logarithmic Sobolev inequality (LSI) -- Universality of the Dyson Brownian motion -- Continuity of local correlation functions -- Universality of Wigner matrices -- Edge universality -- Further results and historical notes |
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| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | ix, 226 Seiten Illustrationen |
| ISBN: | 9781470436483 978-1-4704-3648-3 |