Probability Seminar: Super symmetry approach to the non hermitian random matrices

PROBABILITY, SEMINARS

Speaker:

Mariya Shcherbina - Institute for Low Temperature Physics of National Ukrainian Ac. Sci. (Kharkiv) and Institute for Advanced Study (Princeton)

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 order and discuss the analysis of these representations with a saddle point method.