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On the distribution and fluctuations of eigenvectors of random matrices

Date: Thursday, January 17, 2019 16:00 - 18:00
Speaker: Lucas Benigni (Courant Institute)
Location: Big Seminar room Ground floor / Office Bldg West (I21.EG.101)
Series: Mathematics and CS Seminar
Host: Laszlo Erdos
Contact: WHEATLEY Susanne
Lab building west seminar room

Abstract:

We will study different properties of eigenvectors of random matrices using the dynamical method. In the first part of the talk, I will discuss the distribution and the quantum unique ergodicity property of eigenvectors of deformed Wigner matrices. We will see that eigenvector entries are asymptotically Gaussian with a specific variance localizing them on a small part of the spectrum. The proof relies on a priori local laws for this model and the eigenvector moment flow. In the second part of the talk, I will give some insight in the study of the fluctuations of eigenvectors through the introduction of a new observable following the same eigenvector moment flow.
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