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Random analytic functions via Gaussian multiplicative chaos
- Publication Year :
- 2023
-
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.<br />Comment: 25 pages
- Subjects :
- Mathematics - Probability
Mathematics - Complex Variables
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2306.07732
- Document Type :
- Working Paper