Computable structural formulas for the distribution of the \(\beta\)-Jacobi edge eigenvalues
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Publication:6158137
DOI10.1007/s11139-021-00493-wzbMath1525.15028arXiv2006.02238OpenAlexW3199301705WikidataQ113900568 ScholiaQ113900568MaRDI QIDQ6158137
Peter J. Forrester, Santosh Kumar
Publication date: 31 May 2023
Published in: The Ramanujan Journal (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2006.02238
Random matrices (probabilistic aspects) (60B20) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Recurrences (11B37) Eigenvalues, singular values, and eigenvectors (15A18) Random matrices (algebraic aspects) (15B52)
Cites Work
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- Painlevé representation of Tracy-Widom\(_\beta\) distribution for \(\beta=6\)
- A Fuchsian matrix differential equation for Selberg correlation integrals
- Distribution of the largest root of a matrix for Roy's test in multivariate analysis of variance
- The beta-Jacobi matrix model, the CS decomposition, and generalized singular value problems
- Multivariate analysis and Jacobi ensembles: largest eigenvalue, Tracy-Widom limits and rates of convergence
- The distribution and moments of the smallest eigenvalue of a random matrix of Wishart type
- Fredholm determinants, differential equations and matrix models
- The Calogero-Sutherland model and generalized classical polynomials
- The smallest eigenvalue distribution at the spectrum edge of random matrices
- Optimal soft edge scaling variables for the Gaussian and Laguerre even \(\beta\) ensembles
- Edge scaling of the \(\beta\)-Jacobi ensemble
- Recursion for the smallest eigenvalue density of \(\beta \)-Wishart-Laguerre ensemble
- Extreme eigenvalue distributions of Jacobi ensembles: new exact representations, asymptotics and finite size corrections
- Extreme value statistics of correlated random variables: a pedagogical review
- Recurrence equations for the computation of correlations in the \(1/r^2\) quantum many-body system
- Product of random projections, Jacobi ensembles and universality problems arising from free probability
- Smallest eigenvalue distributions for two classes of β-Jacobi ensembles
- Large deviation eigenvalue density for the soft edge Laguerre and Jacobi β-ensembles
- Hurwitz and the origins of random matrix theory in mathematics
- Theory of Hypergeometric Functions
- Selberg Integrals and Hypergeometric Functions Associated with Jack Polynomials
- Top eigenvalue of a random matrix: large deviations and third order phase transition
- The importance of the Selberg integral
- Difference system for Selberg correlation integrals
- Jacobi Polynomials Associated with Selberg Integrals
- Some Basic Hypergeometric Extensions of Integrals of Selberg and Andrews
- Complex Wishart matrices and conductance in mesoscopic systems: Exact results
- Finite‐size corrections at the hard edge for the Laguerre β ensemble
- On the Numerical Evaluation of Distributions in Random Matrix Theory: A Review
- A review of conjectured laws of total mass of Bacry–Muzy GMC measures on the interval and circle and their applications
- The smallest eigenvalue distribution in the real Wishart–Laguerre ensemble with even topology
- Statistical Theory of the Energy Levels of Complex Systems. V
- Roy’s largest root test under rank-one alternatives
- Quantum conductance problems and the Jacobi ensemble
- On the Marginal Distributions of the Latent Roots of the Multivariate Beta Matrix
- Recursion scheme for the largest $\beta$ -Wishart–Laguerre eigenvalue and Landauer conductance in quantum transport