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Title: Change of variables as a method to study general β-models: Bulk universality

We consider β matrix models with real analytic potentials. Assuming that the corresponding equilibrium density ρ has a one-interval support (without loss of generality σ = [−2, 2]), we study the transformation of the correlation functions after the change of variables λ{sub i} → ζ(λ{sub i}) with ζ(λ) chosen from the equation ζ{sup ′}(λ)ρ(ζ(λ)) = ρ{sub sc}(λ), where ρ{sub sc}(λ) is the standard semicircle density. This gives us the “deformed” β-model which has an additional “interaction” term. Standard transformation with the Gaussian integral allows us to show that the “deformed” β-model may be reduced to the standard Gaussian β-model with a small perturbation n{sup −1}h(λ). This reduces most of the problems of local and global regimes for β-models to the corresponding problems for the Gaussian β-model with a small perturbation. In the present paper, we prove the bulk universality of local eigenvalue statistics for both one-cut and multi-cut cases.
Authors:
 [1]
  1. Institute for Low Temperature Physics Ukr.Ac.Sci, Kharkov, Ukraine and Department of Mathematics, Karazin Kharkov National University (Ukraine)
Publication Date:
OSTI Identifier:
22250810
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 4; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CORRELATION FUNCTIONS; EIGENVALUES; EQUATIONS; EQUILIBRIUM; INTEGRALS; LOSSES; MATRICES; PERTURBATION THEORY; POTENTIALS; STATISTICS; TRANSFORMATIONS