Random analytic functions via Gaussian multiplicative chaos
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.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2023
- DOI:
- arXiv:
- arXiv:2306.07732
- Bibcode:
- 2023arXiv230607732H
- Keywords:
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- Mathematics - Probability;
- Mathematics - Complex Variables
- E-Print:
- 25 pages