Orthogonal and symplectic matrix models: universality and other properties

Abstract

We study orthogonal and symplectic matrix models with polynomial potentials and multi interval supports of the equilibrium measure. For these models we find the bounds (similar to the case of hermitian matrix models) for the rate of convergence of linear eigenvalue statistics and for the variance of linear eigenvalue statistics and find the logarithms of partition functions up to the order O(1). We prove also universality of local eigenvalue statistics in the bulk.

26 pages

References in corpus (5)

• Bulk Universality and Related Properties of Hermitian Matrix Models
• Fluctuations of eigenvalues of matrix models and their applications
• Universality for orthogonal and symplectic Laguerre-type ensembles
• On Universality for Orthogonal Ensembles of Random Matrices
• The dbar steepest descent method for orthogonal polynomials on the real line with varying weights

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• Universality of General $\beta$-Ensembles
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• Bulk universality for deformed Wigner matrices
• Some Open Problems in Random Matrix Theory and the Theory of Integrable Systems. II
• Bulk Universality of General $\beta$-Ensembles with Non-convex Potential
• Optimal local law and central limit theorem for $\beta$-ensembles
• Change of variables as a method to study general $\beta$-models: bulk universality
• Fixed energy universality for generalized Wigner matrices
• Local universality of repulsive particle systems and random matrices
• Asymptotic expansion of beta matrix models in the multi-cut regime
• Particle Systems with Repulsion Exponent $\beta$ and Random Matrices
• Random matrices, log-gases and Holder regularity
• Spacings - An Example for Universality in Random Matrix Theory
• Rigidity of eigenvalues for $\beta$ ensemble in multi-cut regime
• 1D Log Gases and the Renormalized Energy: Crystallization at Vanishing Temperature
• Entropy and the Shannon-McMillan-Breiman theorem for beta random matrix ensembles
• The probability of almost all eigenvalues being real for the elliptic real Ginibre ensemble
• Spacings in Orthogonal and Symplectic Random Matrix Ensembles
• Dynamical Universality for Random Matrices
• Asymptotic properties of the density of particles in $\beta$-ensembles
• Riemann-Hilbert Characterisation of Rational Functions with a General Distribution of Poles on the Extended Real Line Orthogonal with Respect to Varying Exponential Weights: Multi-Point Padé Approximants and Asymptotics