Limiting laws of linear eigenvalue statistics for Hermitian matrix models

DOI10.1063/1.2356796zbMath1112.82022arXivmath/0608719OpenAlexW1502080410MaRDI QIDQ3442064

Leonid Pastur

Publication date: 16 May 2007

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0608719

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Characteristic functions; other transforms (60E10) Eigenvalues, singular values, and eigenvectors (15A18) Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41) Quantum equilibrium statistical mechanics (general) (82B10)

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Cites Work

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• New results on the equilibrium measure for logarithmic potentials in the presence of an external field
• Level spacings distribution for large random matrices: Gaussian fluctuations
• Universality of the local eigenvalue statistics for a class of unitary invariant random matrix ensembles
• Distribution functions for random variables for ensembles of positive Hermitian matrices
• On the statistical mechanics approach in the random matrix theory: Integrated density of states.
• Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model
• Eigenvalue distributions of random unitary matrices
• The central limit theorem for local linear statistics in classical compact groups and related combinatorial identities
• Gaussian limit for determinantal random point fields.
• CLT for linear spectral statistics of large-dimensional sample covariance matrices.
• Universality of the correlations between eigenvalues of large random matrices.
• On fluctuations of eigenvalues of random Hermitian matrices.
• From random matrices to quasi-periodic Jacobi matrices via orthogonal polynomials
• Solution of ordinary differential equations via nonlocal transformations
• Linear functionals of eigenvalues of random matrices
• Mock-Gaussian behaviour for linear statistics of classical compact groups
• Generic behavior of the density of states in random matrix theory and equilibrium problems in the presence of real analytic external fields
• Breakdown of universality in multi-cut matrix models
• Families of equilibrium measures in an external field on the real axis
• On the 1/N corrections to the Green functions of random matrices with independent entries
• Random matrix theory and \(\zeta(1/2+it)\).
• On the \(1/n\) expansion for some unitary invariant ensembles of random matrices