Fluctuations in Various Regimes of Non-Hermiticity and a Holographic
Principle
Fluctuations in Various Regimes of Non-Hermiticity and a Holographic
Principle
We investigate the variance of both smooth linear statistics and rough linear statistics (counting statistics) of random normal matrices. The two classical ensembles of random matrices, the Gaussian unitary ensemble (GUE) and the complex Ginibre ensemble, enjoy an exact map to the ground state of noninteracting Fermions in a harmonic …