|Location:||MSRI: Simons Auditorium, Online/Virtual|
Deformations Of Toeplitz Determinants: Applications, Asymptotics, And Orthogonality Structures
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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
Deformations of Toeplitz Determinants: Applications, Asymptotics, and Orthogonality Structures