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 β 14 Ensembles | 139 |
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Random Matrix Theory: Invariant Ensembles and Universality Percy Deift,Dimitri Gioev Keine Leseprobe verfügbar - 2009 |
Häufige Begriffe und Wortgruppen
Ai(v)dv arcsin asymptotic bounded operator Cauchy-Binet formula Christoffel-Darboux Christoffel-Darboux formula cluster functions CNQN completes the proof compute conclude consider convergence Corollary 6.12 correction terms correlation functions defined denote det(fj det(In diffeomorphism eigenvalues entries equation EXERCISE finite fn(x follows formula Fredholm determinant gap probability hence Hilbert-Schmidt implies integral invertible Jacobian kernel L²(R Lemma log det(1 nonzero norm notation Note Nul(M obtain operator orthogonal and symplectic pairs Pf(A Pf(J Pfaffian probability distribution proof of Theorem proof of universality Proposition prove random matrix theory real symmetric Recall relation REMARK respectively result Section sgno skew skew-symmetric matrix statistics symplectic ensembles Theorem 6.7 trace class uniformly Widom's XCP/CO μη σΗ