Smallest Dirac Eigenvalue Distribution from Random Matrix Theory

TL;DR

This paper derives the distribution of the smallest eigenvalue of chiral Hermitian random matrices relevant to QCD, linking it to the QCD partition function and demonstrating universality with the Bessel kernel.

Contribution

It provides explicit formulas for the smallest eigenvalue distribution in chiral random matrix ensembles and establishes their universality in the mesoscopic regime.

Findings

Derived the hole probability and smallest eigenvalue distribution

Connected eigenvalue distribution to QCD partition function

Established universality with the microscopic Bessel kernel

Abstract

We derive the hole probability and the distribution of the smallest eigenvalue of chiral hermitian random matrices corresponding to Dirac operators coupled to massive quarks in QCD. They are expressed in terms of the QCD partition function in the mesoscopic regime. Their universality is explicitly related to that of the microscopic massive Bessel kernel.