Super symmetry approach to the non hermitian random matrices: deformed Ginibre ensemble
Super symmetry approach to the non hermitian random matrices: deformed Ginibre ensemble
-
Mariya Shcherbina, Institute for Low Temperature Physics of Ukrainian National Academy of Science & IAS
We consider a complex Ginibre ensemble of random matrices with a deformation $H=H_0+A$, where $H_0$ is a Gaussian complex Ginibre matrix and $A$ is a rather general deformation matrix. The analysis of such ensemble is motivated by many problems of random matrix theory and its applications. We use the Grassmann integration methods to obtain integral representation of spectral correlation functions of the first and the second 听order and discuss the analysis of these representations with 听a saddle point method. Applications 听of such an analysis to the problems of local regime of the deformed Ginibre ensemble 听will be discussed.