Deformed Ginibre ensembles and integrable systems

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.