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Random Toeplitz matrices

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Random Toeplitz matrices belong to the exciting area that lies at the intersection of the usual Wigner random matrices and random Schrodinger operators. In this talk I will describe two recent results on random Toeplitz matrices. First, the maximum eigenvalue, suitably normalized, converges to the 2-4 operator norm of the well-known Sine-kernel. Second, the limiting eigenvalue distribution is absolutely continuous, which partially settles a conjecture made by Bryc, Dembo and Jiang (2006). I will also present several open questions and conjectures.

This is joint work with Balint Virag (Toronto).

This talk is part of the Probability series.

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1 Hicks & Mead Rooms, University Centre, Granta Place Online via zoom & Kings Hedges Room

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