Deformed Ginibre ensembles and integrable systems

TL;DR

This paper explores deformed Ginibre ensembles across real, complex, and quaternion-real cases, linking their partition functions to integrable systems through fermionic expectation values and introducing double deformed Dyson-Wigner ensembles.

Contribution

It presents a novel fermionic representation of deformed Ginibre ensembles and introduces double deformed Dyson-Wigner ensembles, expanding the understanding of their integrable structures.

Findings

Partition functions expressed as fermionic expectation values.

Comparison of fermionic representations between Ginibre and Dyson-Wigner ensembles.

Introduction of double deformed Dyson-Wigner ensembles.

Abstract

We consider three Ginibre ensembles (real, complex and quaternion-real) with a deformed measure and relate them to the known integrable systems via presenting partition functions of these ensembles in form of fermionic expectation values. We also introduce double deformed Dyson-Wigner ensembles and compare their fermionic representations with these of Ginibre ensembles.