Bécs-Budapest Valószínűségszámítási Szeminárium

Abstract:  It is well known that eigenvalues of general non-Hermitian matrices can be very unstable under tiny perturbations but adding a small noise regularises this instability. The quantity governing this effect, called the eigenvalue condition number in numerical linear algebra, is also well known in random matrix theory as the eigenvector overlap. We present several recent results on almost optimal lower and upper bounds on this key quantity. For the lower bound we need to prove the strong form of quantum unique ergodicity (QUE) for the singular vectors of non-Hermitian random matrices. The upper bound requires very different tools: here we prove a Wegner type estimate for non-Hermitian matrices. The talk is based upon joint works with G. Cipolloni, J. Henheik, H.-C. Ji, O. Kolupaiev and D. Schroder.

A részletes program:
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