The Riemann-Hilbert approach to the determinants of Toeiplitz + Hankel matrices

Alexander Its
Indiana University Purdue University, Indianapolis
Wednesday, May 16, 2018 - 16:00

During the last 10-15 years the Riemann-Hilbert technique has been successfully used for solving a number of long-standing problems in the field of  asymptotic analysis of the determinants of Toeplitz and  Hankel matrices. The technique has been also extended to the determinants of Toelpitz + Hankel matrices generated by the same symbol. In the talk, we will explain how the Riemann-Hilbert framework can be further extended to include the Toeplit+Hankel matrices whose symbols are unrelated. The principal motivation of this extension is the evaluation of the large N asymptotics of the eigenvalues of Hankel matrices. The talk is based on the joint work with R. Gharakhloo, and it is a part of bigger joint project with P. Deift, T. Bothner and I. Krasovsky on the asymptotic theory of Toeplitz, Hankel and Toplitz + Hankel determinants.

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