Thursday, April 17, 2008 at 3:00 PM in HA 330
Professor Wlodek Bryc, University of Cincinnati
Spectra of Large Random Toeplitz Matrices
As the dimension tends to infinity, spectral measures of large random Toeplitz matrices with independent identically distributed entries that have finite second moments converge to the \\\"universal\\\" measure on R. I will review the main ideas in the proof, and what is known as well as what is not known about the limiting measure. I will also talk about similar results for other \\\"structured\\\" ensembles of symmetric random matrices, including the \\\"trivial cases\\\" of symmetric circulant and \\\"reversed circulant\\\" matrices.
If time permits, I will then talk about \\\"block-Toeplitz\\\" matrices where the limits of spectral measures are determined from the system of equations stated by Girko, and which in \\\"modern approach\\\" arises from matrix-valued free probability.
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Seminar Organizer: Min Kang