Chiral Random Matrix Model at Finite Chemical Potential: Characteristic Determinant and Edge Universality

Understand

We derive an exact formula for the stochastic evolution of the characteristic determinant of a class of deformed Wishart matrices following from a chiral random matrix model of QCD at finite chemical potential.

• In the WKB approximation, the characteristic determinant describes a sharp droplet of eigenvalues that deforms and expands at large stochastic times.
• Beyond the WKB limit, the edges of the droplet are fuzzy and described by universal edge functions.
• At the chiral point, the characteristic determinant in the microscopic limit is universal.