# Logarithmic Universality in Random Matrix Theory

Source: [Logarithmic Universality in Random Matrix Theory](<https://www.sota2.com/research/paper/68fa24aa2c2a3760193a7575>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T09:25:30.179Z

Authors: K. Splittorff

Published: 1998-10-30T13:19:22.000Z

## 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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/hep-th/9810248>)

[PDF](<https://arxiv.org/pdf/hep-th/9810248.pdf>)