Linear differential equations for the resolvents of the classical matrix ensembles
From MaRDI portal
Publication:5019010
DOI10.1142/S2010326322500034zbMath1480.15043arXiv1908.04963OpenAlexW3103583818MaRDI QIDQ5019010
Anas A. Rahman, Peter J. Forrester
Publication date: 27 December 2021
Published in: Random Matrices: Theory and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1908.04963
resolventeigenvalue densitySelberg integralclassical ensembleshard and soft edge scalingmoment recurrences
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Eigenvalues, singular values, and eigenvectors (15A18) Random matrices (algebraic aspects) (15B52) Qualitative investigation and simulation of ordinary differential equation models (34C60)
Related Items
Expanding the Fourier transform of the scaled circular Jacobi \(\beta\) ensemble density, Convergence rate to the Tracy-Widom laws for the largest eigenvalue of sample covariance matrices, Quantitative Tracy-Widom laws for the largest eigenvalue of generalized Wigner matrices, Differential identities for the structure function of some random matrix ensembles, Moments of the ground state density for the d-dimensional Fermi gas in an harmonic trap, Relations between moments for the Jacobi and Cauchy random matrix ensembles, The classical β-ensembles with β proportional to 1/N: From loop equations to Dyson’s disordered chain
Cites Work
- Unnamed Item
- Unnamed Item
- Moments of the position of the maximum for GUE characteristic polynomials and for log-correlated Gaussian processes
- The right tail exponent of the Tracy-Widom \(\beta\) distribution
- Asymptotic forms for hard and soft edge general \(\beta \) conditional gap probabilities
- A Fuchsian matrix differential equation for Selberg correlation integrals
- A recursion formula for the moments of the Gaussian orthogonal ensemble
- Hermite and Laguerre \(\beta\)-ensembles: asymptotic corrections to the eigenvalue density
- Duality in random matrix ensembles for all \(\beta \)
- Multivariate analysis and Jacobi ensembles: largest eigenvalue, Tracy-Widom limits and rates of convergence
- Duality of real and quaternionic random matrices
- The Calogero-Sutherland model and generalized classical polynomials
- Duality of orthogonal and symplectic matrix integrals and quaternionic Feynman graphs
- Random matrices with complex Gaussian entries
- Asymptotic correlations at the spectrum edge of random matrices
- Classical skew orthogonal polynomials and random matrices
- A convergent \({\frac{1}{N}}\) expansion for GUE
- Optimal soft edge scaling variables for the Gaussian and Laguerre even \(\beta\) ensembles
- Differential operators and spectral distributions of invariant ensembles from the classical orthogonal polynomials. {T}he continuous case
- The Euler characteristic of the moduli space of curves
- On the distribution of the largest eigenvalue in principal components analysis
- Rectangular matrix models and combinatorics of colored graphs
- Asymptotic expansion of \(\beta \) matrix models in the one-cut regime
- Edge scaling of the \(\beta\)-Jacobi ensemble
- The spectrum edge of random matrix ensembles.
- Generalisations of the Harer-Zagier recursion for 1-point functions
- Integer moments of complex Wishart matrices and Hurwitz numbers
- Moments of random matrices and hypergeometric orthogonal polynomials
- MOPS: multivariate orthogonal polynomials (symbolically)
- The rate of convergence for spectra of GUE and LUE matrix ensembles
- Recurrence equations for the computation of correlations in the \(1/r^2\) quantum many-body system
- Counting formulas associated with some random matrix averages
- Large-N expansion for the time-delay matrix of ballistic chaotic cavities
- Moments of the transmission eigenvalues, proper delay times, and random matrix theory. I
- Moments of the transmission eigenvalues, proper delay times and random matrix theory II
- Large deviation eigenvalue density for the soft edge Laguerre and Jacobi β-ensembles
- ASYMPTOTIC EXPANSIONS FOR THE GAUSSIAN UNITARY ENSEMBLE
- Correlators for the Wigner–Smith time-delay matrix of chaotic cavities
- Selberg Integrals and Hypergeometric Functions Associated with Jack Polynomials
- Moments of the Gaussian β ensembles and the large-N expansion of the densities
- Spectral density asymptotics for Gaussian and Laguerre β-ensembles in the exponentially small region
- Moments of the ground state density for the d-dimensional Fermi gas in an harmonic trap
- Asymptotic corrections to the eigenvalue density of the GUE and LUE
- Asymptotic form of the density profile for Gaussian and Laguerre random matrix ensembles with orthogonal and symplectic symmetry
- Global spectrum fluctuations for the β-Hermite and β-Laguerre ensembles via matrix models
- Selberg integrals, super-hypergeometric functions and applications to β-ensembles of random matrices
- Difference system for Selberg correlation integrals
- Exact and asymptotic local virial theorems for finite fermionic systems
- Random matrix ensembles with an effective extensive external charge
- Exact results and universal asymptotics in the Laguerre random matrix ensemble
- Harmonically trapped fermion gases: exact and asymptotic results in arbitrary dimensions
- Functional form for the leading correction to the distribution of the largest eigenvalue in the GUE and LUE
- Topological recursion for irregular spectral curves
- Large N expansions for the Laguerre and Jacobi β-ensembles from the loop equations
- GLOBAL FLUCTUATIONS FOR LINEAR STATISTICS OF β-JACOBI ENSEMBLES
- Topological recursion in enumerative geometry and random matrices
- Asymptotic analysis of singular values of rectangular complex matrices in the Laguerre and fixed-trace ensembles
- Moments of the eigenvalue densities and of the secular coefficients ofβ-ensembles
- Moments of Wishart-Laguerre and Jacobi ensembles of random matrices: application to the quantum transport problem in chaotic cavities
- Transmission eigenvalue densities and moments in chaotic cavities from random matrix theory
