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Random analytic functions via Gaussian multiplicative chaos

Yichao Huang,Eero Saksman

arXiv (Cornell University)（2023）

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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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Key words
gaussian multiplicative chaos,random analytic functions
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