Gergen Lectures, Fall_2012
https://services.math.duke.edu/mcal?listgroup-6
Gergen Lectures Upcoming Seminarsen-usSun, 17 Jan 2021 17:17:49 ESThttps://services.math.duke.edu/mcal2015-01-01T12:00:00-05002dailyThe spectrum of non-normal matrices
https://services.math.duke.edu/mcal?abstract-7802
In this talk we will give an introduction to spectral properties of
non-normal matrices, that is matrices which do not commute with their adjoint. A well known example of non-normal random matrices is simply given by a square matrix with independent and equidistributed entries. It was shown in a series of papers by Girko, Bai and culminating with a work by Tao and Vu that the spectrum of such matrix is asymptotically distributed according to the uniform measure on the disc. In this talk, we will discuss the properties of the spectrum of more general non-normal random matrices. In particular we will will consider those whose law is invariant under multiplication by unitary matrices and show that the support of the spectrum is then always a ring, as conjectured by Feinberg and Zee. No previous experience with random matrices is needed to follow this talk.Alice Guionnet Wed, 17 Oct 2012 16:30:00 EDT7802Gergen LecturesprobabilityGergen Lectures SeminarFall, 2012Wednesday, October 17, 2012, 4:30pmWed, 17 Oct 2012 17:30:00 EDT130 PhysicsThe spectrum of non-normal matrices, II: the Brown measure.
https://services.math.duke.edu/mcal?abstract-7803
In this talk, which is a continuation of Wednesday's lecture, we shall describe the natural candidate for the limit of the empirical measure of the eigenvalues of non-normal matrices, the so-called Brown measure. We will give some details about how to prove convergence towards such a limit, but also discuss the instability of such convergence.Alice Guionnet Thu, 18 Oct 2012 16:30:00 EDT7803Gergen LecturesprobabilityGergen Lectures SeminarFall, 2012Thursday, October 18, 2012, 4:30pmThu, 18 Oct 2012 17:30:00 EDT119 Physics