Random analytic functions via Gaussian multiplicative chaos

Eero Saksman; Yichao Huang

Random analytic functions via Gaussian multiplicative chaos

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arxiv 2306.07732 v1 pith:VOIXXTM4 submitted 2023-06-13 math.PR math.CV

Yichao Huang , Eero Saksman This is my paper · ORCID

classification math.PRmath.CV

keywords analyticgaussianmultiplicativerandomvarphialmostblaschkechaos

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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.

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Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC
math.PR 2024-11 accept novelty 8.0 of 10

For every sub-critical 1D Gaussian multiplicative chaos measure, the Fourier dimension equals the correlation dimension: 1-γ² for small γ, (√2-γ)² for large γ.

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