Kac-Rice approach to non-Hermitian random matrices

by Yan Fyodorov

Friday Apr 11, 2025, 4:15 PM → 6:15 PM Europe/Berlin

D5-153 (UHG)

Non-Hermitian random matrices attracted considerable interestin recent years as a tool to characterize Quantum Chaos in dissipative systems. Beyond the framework of standard Ginibre ensembles one of the general tools available for studying such matrices is the "Hermitization Trick" due to Girko.  I will describe an alternative approach based on Kac-Rice formula which provides access not only to eigenvalues but also to nontrivial eigenvectors of non-Hermitian random matrices. To illustrate this approach I will consider a family of matrices interpolating  between complex Ginibre and real Ginibre ensembles, which in particular allows to reveal a new scaling regime of "weak complexity".