Random analytic functions via Gaussian multiplicative chaos

Yichao Huang; Eero Saksman

doi:10.4310/ARKIV.2025.v63.n2.a4

Random analytic functions via Gaussian multiplicative chaos

Yichao Huang
, Eero Saksman

Research output: Contribution to journal › Article › peer-review

Abstract

We define a random analytic function φ on the unit disc by letting a Gaussian multiplicative chaos measure to be one of its Clark measures. We show that φ is almost surely a Blaschke product and we provide rather sharp estimates for the density of its zeroes.

Original language	English
Pages (from-to)	279-309
Number of pages	31
Journal	Arkiv for Matematik
Volume	63
Issue number	2
DOIs	https://doi.org/10.4310/ARKIV.2025.v63.n2.a4
Publication status	Published - Oct 2025
Externally published	Yes

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10.4310/ARKIV.2025.v63.n2.a4

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Random analytic functions via Gaussian multiplicative chaos

Abstract

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