Seminarium KMMF "Teoria Dwoistości"

The empirical spectral distribution of a non-hermitian random matrix concentrates around a deterministic probability distribution on the complex plane as its dimension increases. Despite the inherent spectral instability of such models, this approximation is valid all the way down to local scales just above the typical eigenvalue spacing distance. We will give an overview over some basic questions and techniques associated with the study of spectra for non-hermitian random matrices. Furthermore, we will present recent results for matrices with correlated entries and their application to systems of randomly coupled differential equations that are used to model a wide range of disordered dynamical systems ranging from neural networks to food webs. To join our online seminar, use the Zoom identificator: https://us02web.zoom.us/j/8145917621?pwd=bVVKend0SHFKNUNyUUQ4cWNRK3laZz09