Wednesday, October 17, 2012, 4:30pm, 130 Physics

Alice Guionnet

- 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.

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