Speaker
Benigni, The delocalization of eigenvectors of real elliptic matrices
Abstract
Eigenvectors of non-Hermitian random matrices are typically delocalized, but in real ensembles this delocalization is not uniform across the spectrum. In particular, eigenvectors whose eigenvalues lie close to the real axis are more localized than those in the complex bulk. In this talk, I will discuss this phenomenon for the real elliptic Ginibre ensemble. Using the Schur decomposition, we compute the limiting distribution of the inverse participation ratio of an eigenvector conditioned on the position of its eigenvalue. The result describes a sharp transition in the depletion regime from real-vector behavior near the real axis to complex-vector behavior in the bulk. This is a joint work with Simon Coste and Guillaume Dubach.