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## Publications [#357478] of Hau-Tieng Wu

Papers Published

1. Steinerberger, S; Wu, H-T, On Zeroes of Random Polynomials and an Application to Unwinding, International Mathematics Research Notices, vol. 2021 no. 13 (June, 2021), pp. 10100-10117, Oxford University Press (OUP) [doi]
(last updated on 2021/10/16)

Abstract:
Abstract Let $\mu$ be a probability measure in $\mathbb{C}$ with a continuous and compactly supported density function, let $z_1, \dots , z_n$ be independent random variables, $z_i \sim \mu$, and consider the random polynomial $p_n(z) = \prod _{k=1}^{n}{(z - z_k)}.$ We determine the asymptotic distribution of $\left \{z \in \mathbb{C}: p_n(z) = p_n(0)\right \}$. In particular, if $\mu$ is radial around the origin, then those solutions are also distributed according to $\mu$ as $n \rightarrow \infty$. Generally, the distribution of the solutions will reproduce parts of $\mu$ and condense another part on curves. We use these insights to study the behavior of the Blaschke unwinding series on random data.

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