Universality of General $\beta$-Ensembles

Abstract

We prove the universality of the $\beta$-ensembles with convex analytic potentials and for any $\beta >0$, i.e. we show that the spacing distributions of log-gases at any inverse temperature $\beta$ coincide with those of the Gaussian $\beta$-ensembles.

Sep 21, 2011: Lemma 3.9 was corrected. Feb 5: Some typos in Lemma 5.9 were corrected

References in corpus (4)

• Spectral Statistics of Erd{\H o}s-Rényi Graphs II: Eigenvalue Spacing and the Extreme Eigenvalues
• Bulk Universality and Related Properties of Hermitian Matrix Models
• Bulk Universality of General $\beta$-Ensembles with Non-convex Potential
• Orthogonal and symplectic matrix models: universality and other properties

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• Stability of the Matrix Dyson Equation and Random Matrices with Correlations
• Universality of the Stochastic Airy Operator
• Optimal local law and central limit theorem for $\beta$-ensembles
• Local density for two-dimensional one-component plasma
• The Sine${}_{\beta }$ operator
• Local universality of repulsive particle systems and random matrices
• The high temperature crossover for general 2D Coulomb gases
• Harmonic analysis in phase space and finite Weyl-Heisenberg ensembles
• Poisson statistics for beta ensembles on the real line at high temperature
• Repulsion in low temperature $\beta$-ensembles
• Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case
• Dynamical Bulk Scaling limit of Gaussian Unitary Ensembles and Stochastic Differential Equation gaps
• Quenched universality for deformed Wigner matrices
• On the Spectrum of Random Anti-symmetric and Tournament Matrices
• Buses of Cuernavaca - an agent-based model for universal random matrix behavior minimizing mutual information
• A matrix model of a non-Hermitian $\beta$-ensemble
• Palm measures for Dirac operators and the Sine beta process