Probabilistic Padé Problems

Abstract: It has been observed, by Froissart (1969), that zeros and poles of higher order Padé approximants of random perturbations of a deterministic Taylor series tend to form unstable pairs. These pairs appear at loci characteristic of the random part in the coefficients of the Taylor series. While this phenomenon has only been confirmed experimentally, it has been suggested, and indeed used, as a noise detection tool. In this talk we will explain how techniques from high-dimensional probability and logarithmic potential theory can be melted together to rigorously establish and quantify the clustering of zeros in the ``pure noise’’ case, when the coefficients are drawn according to a distribution with anti-concentration properties.

Based on a joint ongoing work with S. Dostoglou (University of Missouri).

functional analysisoperator algebras

Audience: advanced learners

Functional analysis and operator algebras in Athens

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