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arXiv · 2306.07732

Random analytic functions via Gaussian multiplicative chaos

Yichao Huang·Eero Saksman
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Abstract

We define a random analytic function $\varphi$ on the unit disc by letting a Gaussian multiplicative measure to be one of its Clark measures. We show that $\varphi$ is almost surely a Blaschke product and we provide rather sharp estimates for the density of its zeroes.

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Yichao Huang, Eero Saksman. 2023-06-13. Random analytic functions via Gaussian multiplicative chaos. https://arxiv.org/abs/2306.07732

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