The polyanalytic Ginibre ensembles

TL;DR

This paper introduces a polyanalytic extension of the Ginibre ensemble to model higher Landau levels, analyzing the local behavior of the resulting point process under blow-up scaling.

Contribution

It presents a novel polyanalytic generalization of the Ginibre ensemble and investigates its local properties, extending understanding beyond the lowest Landau level.

Findings

Characterization of local behavior of the polyanalytic Ginibre ensemble

Extension of Landau level modeling in random matrix theory

Insights into the structure of higher Landau level point processes

Abstract

We consider a polyanalytic generalization of the Ginibre ensemble. This models allowing higher Landau levels (the Ginibre ensemble corresponds to the lowest Landau level). We study the local behavior of this point process under blow-ups.