Random Matrix Theory: Invariant Ensembles and UniversalityAmerican Mathematical Soc., 01.01.2009 - 217 Seiten "This book features a unified derivation of the mathematical theory of the three classical types of invariant random matrix ensembles-orthogonal, unitary, and symplectic. The authors follow the approach of Tracy and Widom, but the exposition here contains a substantial amount of additional material, in particular, facts from functional analysis and the theory of Pfaffians. The main result in the book is a proof of universality for orthogonal and symplectic ensembles corresponding to generalized Gaussian type weights following the authors' prior work. New, quantitative error estimates are derived." --Book Jacket. |
Inhalt
Three Classes of Invariant Ensembles | 9 |
Auxiliary Facts from Functional Analysis Pfaffians | 37 |
Eigenvalue Statistics for the Three Types of Ensembles | 65 |
Widoms Formulae for the ˇ D 1 and 4 Correlation Kernels | 115 |
Large N Eigenvalue Statistics for the B 1 4 Ensembles | 139 |
113 | 169 |
Bibliography | 211 |
| 217 | |
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Random Matrix Theory: Invariant Ensembles and Universality Percy Deift,Dimitri Gioev Keine Leseprobe verfügbar - 2009 |
Häufige Begriffe und Wortgruppen
ˇ ˇ ˇ Ä j Ä Ai(t)dt Airy asymptotics bounded Cauchy-Binet formula Christoffel-Darboux Christoffel-Darboux formula cluster functions CNIN compact set completes the proof compute convergence Corollary 6.12 correction terms correlation functions defined denote det2 double integrals eigenvalues error estimates EXERCISE finite follows formulae Fredholm determinant gap probability HCDH hence Hermitian self-dual Hilbert-Schmidt implies invertible kernel Lemma Math NiD1 norm notation Note obtain operator orthogonal and symplectic orthogonal polynomials patience sorting Pfaffian Phys polynomial proof of Theorem proof of universality Proposition prove random matrix random matrix theory Recall REMARK scaling Section skew-symmetric skew-symmetric matrix statistics symplectic ensembles Theorem 6.7 trace class Tracy-Widom distribution uniformly unitary Widom λν,β हु