Seminar
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| Location: | SLMath: Eisenbud Auditorium, Online/Virtual |
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification
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Secondary Mathematics Subject Classification
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Deformations Of Toeplitz Determinants: Applications, Asymptotics, And Orthogonality Structures
To participate in this seminar, please register HERE.
Structured moment determinants arise in numerous applications, especially in random matrix theory and statistical mechanics. Aside from the (pure) Toeplitz and Hankel determinants, there has been a growing interest in recent years in studying other deformed structured moment determinants. Among those are Toeplitz+Hankel, bordered Toeplitz, and "2j-k"\"j-2k" determinants. In my talk, I will try to describe some aspects of these structured determinants mainly focusing on:
- Connection of bordered Toeplitz determinants with the solution of the Baik-Deift-Johansson Riemann-Hilbert problem for biorthogonal polynomials on the unit circle, the strong Szego limit theorem for a class of bordered Toeplitz determinants, and the next-to-diagonal correlations of Ising model in the low-temperature regime. (joint work with A.Its, E.Basor, T.Ehrhardt, Y.Li) https://arxiv.org/abs/2011.14561
- The orthogonality structures, recurrence relations, multiple integral formulae, and the Christoffel-Darboux identities for the 2j-k and j-2k systems. These determinants are related to asymptotic formulae for averages of derivatives of characteristic polynomials over the groups USp(2N), SO(2N), and O^-(2N). (joint work with N.Witte) https://arxiv.org/abs/2106.15079
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Deformations of Toeplitz Determinants: Applications, Asymptotics, and Orthogonality Structures
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