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Mathematics & Statistics

Classical Analysis
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Friday, January 18, 2019


Planar orthogonal polynomials with multiple logarithmic singularities in the potential
Seung-Yeop Lee
CMC 130


We consider the large degree asymptotic behavior of the planar orthogonal polynomials when the orthogonality measure is given by the exponent of the sum of logarithmic singularities whose locations can be arbitrary. The limiting locus of the roots of the orthogonal polynomials is given in terms of the locus of the roots for the single pole case, that has been known previously. The Riemann-Hilbert formulation makes possible both the numerical support and the proof of the fact. This is a joint work with Meng Yang (UC Louvain, Belgium).