English

Random analytic functions via Gaussian multiplicative chaos

Probability 2023-06-14 v1 Complex Variables

Abstract

We define a random analytic function φ\varphi on the unit disc by letting a Gaussian multiplicative measure to be one of its Clark measures. We show that φ\varphi 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}
}

Comments

25 pages

R2 v1 2026-06-28T11:03:51.990Z