Logarithmic Universality in Random Matrix Theory

Abstract

Universality in unitary invariant random matrix ensembles with complex matrix elements is considered. We treat two general ensembles which have a determinant factor in the weight. These ensembles are relevant, e.g., for spectra of the Dirac operator in QCD. In addition to the well established universality with respect to the choice of potential, we prove that microscopic spectral correlators are unaffected when the matrix in the determinant is replaced by an expansion in powers of the matrix. We refer to this invariance as logarithmic universality. The result is used in proving that a simple random matrix model with Ginsparg-Wilson symmetry has the same microscopic spectral correlators as chiral random matrix theory.

16 pages, latex2e

References in corpus (6)

• Exact chiral symmetry on the lattice and the Ginsparg-Wilson relation
• More about exactly massless quarks on the lattice
• Multicritical Microscopic Spectral Correlators of Hermitian and Complex Matrices
• Universal Massive Spectral Correlators and QCD_3
• Odd-flavored QCD_3 and Random Matrix Theory
• The Ginsparg-Wilson relation and local chiral random matrix theory

Cited by in corpus (9)

• Random Matrix Theory and Chiral Symmetry in QCD
• Factorization of Correlation Functions and the Replica Limit of the Toda Lattice Equation
• The Scaling of Exact and Approximate Ginsparg-Wilson Fermions
• The Spectral Density of the QCD Dirac Operator and Patterns of Chiral Symmetry Breaking
• Spectral Properties of the Overlap Dirac Operator in QCD
• A Random Matrix Model for Color Superconductivity at Zero Chemical Potential
• Spectral Universality of Real Chiral Random Matrix Ensembles
• New Critical Matrix Models and Generalized Universality
• The zeros of the QCD partition function