We review the development of random-matrix theory (RMT) during the last fifteen years. We
emphasize both the theoretical aspects, and the application of the theory to a number of …

▪ Abstract Random matrix theory is a powerful way to describe universal correlations of
eigenvalues of complex systems. It also may serve as a schematic model for disorder in …

We study the spectrum of the QCD Dirac operator by means of the valence quark mass
dependence of the chiral condensate in partially quenched Chiral Perturbation Theory …

Eigenvalues and eigenfunctions of the QCD Dirac operator are studied for gauge field
configurations given by a liquid of instantons. We find that for energy differences δE below …

At zero temperature the lowest part of the spectrum of the QCD Dirac operator is known to
consist of delocalized modes that are described by random matrix statistics. In the present …

We study the effects of taste degeneracy on the continuum scaling of the localization
properties of the staggered Dirac operator in high-temperature QCD using numerical …

We introduce three universality classes of chiral random matrix ensembles with a nonzero
chemical potential and real, complex or quaternion real matrix elements. In the …

Using the graded eigenvalue method a rea recently computed extension of the Itzykysn-
Zuber integral to complex matrices, we compute the k-point spectral correlation functions of …

The presence of a chemical potential completely changes the analytical structure of the QCD
partition function. In particular, the eigenvalues of the Dirac operator are distributed over a …

Random matrix theory (RMT) is a powerful statistical tool to model spectral fluctuations. This
approach has also found fruitful application in quantum chromodynamics (QCD) …