arXiv:2306.07732 Abstract | arXiv Analytics

arXiv:2306.07732 [math.PR]Abstract References Reviews Resources

Random analytic functions via Gaussian multiplicative chaos

Published 2023-06-13Version 1

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.

Comments: 25 pages

Categories: math.PR, math.CV

Keywords: random analytic function, gaussian multiplicative chaos, unit disc, blaschke product, sharp estimates

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