The mean spectral measures of random Jacobi matrices related to Gaussian beta ensembles

Abstract

An explicit formula for the mean spectral measure of a random Jacobi matrix is derived. The matrix may be regarded as the limit of Gaussian beta ensemble (G$\beta$E) matrices as the matrix size $N$ tends to infinity with the constraint that $N\beta$ is a constant.

References in corpus (4)

• Matrix Models for Beta Ensembles
• Global spectrum fluctuations for the $\beta$-Hermite and $\beta$-Laguerre ensembles via matrix models
• Moments of the Gaussian $\beta$ Ensembles and the large-$N$ expansion of the densities
• An exactly solvable self-convolutive recurrence

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• Beta Jacobi ensembles and associated Jacobi polynomials
• The high temperature crossover for general 2D Coulomb gases
• On the mean Density of States of some matrices related to the beta ensembles and an application to the Toda lattice
• Rank one HCIZ at high temperature: interpolating between classical and free convolutions
• The classical $\beta$-ensembles with $\beta$ proportional to $1/N$: from loop equations to Dyson's disordered chain
• Matrix addition and the Dunkl transform at high temperature
• Classical beta ensembles and related eigenvalues processes at high temperature and the Markov--Krein transform
• Universality of global asymptotics of Jack-deformed random Young diagrams at varying temperatures