Random analytic functions via Gaussian multiplicative chaos
Probability
2023-06-14 v1 Complex Variables
Abstract
We define a random analytic function on the unit disc by letting a Gaussian multiplicative measure to be one of its Clark measures. We show that is almost surely a Blaschke product and we provide rather sharp estimates for the density of its zeroes.
Keywords
Cite
@article{arxiv.2306.07732,
title = {Random analytic functions via Gaussian multiplicative chaos},
author = {Yichao Huang and Eero Saksman},
journal= {arXiv preprint arXiv:2306.07732},
year = {2023}
}
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25 pages