High–low temperature dualities for the classical β-ensembles

DOI10.1142/S2010326322500356zbMath1500.37011arXiv2103.11250OpenAlexW4226181964WikidataQ114071593 ScholiaQ114071593MaRDI QIDQ5041688

Peter J. Forrester

Publication date: 14 October 2022

Published in: Random Matrices: Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.11250

zbMATH Keywords

duality relationsloop equationsclassical ensemblesStieltjes electrostatics

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Dynamical systems and their relations with probability theory and stochastic processes (37A50) Random matrices (algebraic aspects) (15B52) Generation, random and stochastic difference and differential equations (37H10) Dynamical aspects of statistical mechanics (37A60)

Related Items

Generalized Gibbs ensemble of the Ablowitz-Ladik lattice, circular \(\beta\)-ensemble and double confluent Heun equation, Expanding the Fourier transform of the scaled circular Jacobi \(\beta\) ensemble density, \(\beta\)-ensembles and higher genera Catalan numbers

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Wigner matrices, the moments of roots of Hermite polynomials and the semicircle law
• Resolvents and Seiberg-Witten representation for a Gaussian \(\beta\)-ensemble
• The mean spectral measures of random Jacobi matrices related to Gaussian beta ensembles
• Central limit theorems for multivariate Bessel processes in the freezing regime
• Loop equation analysis of the circular \(\beta\) ensembles
• Interpretations of some parameter dependent generalizations of classical matrix ensembles
• Asymptotic expansion of \(\beta \) matrix models in the one-cut regime
• Limit theorems for multivariate Bessel processes in the freezing regime
• Beta Jacobi ensembles and associated Jacobi polynomials
• Limits and fluctuations of \(p\)-adic random matrix products
• The high temperature crossover for general 2D Coulomb gases
• Central limit theorems for multivariate Bessel processes in the freezing regime. II. The covariance matrices
• Recurrence equations for the computation of correlations in the \(1/r^2\) quantum many-body system
• Eigenvalues of Hermite and Laguerre ensembles: large beta asymptotics
• General β-Jacobi Corners Process and the Gaussian Free Field
• Interacting particles on the line and Dunkl intertwining operator of typeA: application to the freezing regime
• Moments of the Gaussian β ensembles and the large-N expansion of the densities
• Large deviations of the maximal eigenvalue of random matrices
• Associated Laguerre and Hermite polynomials
• Electrostatic equilibria on the unit circle via Jacobi polynomials
• Global spectrum fluctuations for the β-Hermite and β-Laguerre ensembles via matrix models
• Large N expansions for the Laguerre and Jacobi β-ensembles from the loop equations
• Matrix models for beta ensembles
• Invariant β-Wishart ensembles, crossover densities and asymptotic corrections to the Marčenko–Pastur law
• Limit theorems and soft edge of freezing random matrix models via dual orthogonal polynomials
• Functional central limit theorems for multivariate Bessel processes in the freezing regime
• The classical β-ensembles with β proportional to 1/N: From loop equations to Dyson’s disordered chain
• Gaussian Approximation of the Distribution of Strongly Repelling Particles on the Unit Circle
• Crystallization of Random Matrix Orbits
• The uses of the refined matrix model recursion
• Moments of the eigenvalue densities and of the secular coefficients ofβ-ensembles
• Analytic properties of the structure function for the one-dimensional one-component log-gas.