Thursday, November 18, 2021
Time | Items |
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All day |
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4:00pm |
11/18/2021 - 4:00pm Location:
https://yale.zoom.us/j/99019019033 (password was emailed by Ivan)
11/18/2021 - 4:15pm Abstract: In this talk, I will present joint work with Benjamin Eichinger and Brian Simanek: a new approach to universality limits for orthogonal polynomials on the real line which is completely local and uses only the boundary behavior of the Weyl m-function at the point. We show that bulk universality of the Christoffel–Darboux kernel holds for any point where the imaginary part of the m-function has a positive finite nontangential limit. This approach is based on studying a matrix version of the Christoffel–Darboux kernel and the realization that bulk universality for this kernel at a point is equivalent to the fact that the corresponding m-function has normal limits at the same point. Our approach automatically applies to other self-adjoint systems with 2x2 transfer matrices such as continuum Schrodinger and Dirac operators. We also obtain analogous results for orthogonal polynomials on the unit circle. Location: |