Multiplicative chaos measures for a random model of the Riemann zeta function

2016/04/28 by Saksman, Eero, Webb, Christian · 1 citation
#FOS: Mathematics #Number Theory (math.NT) #Probability (math.PR)

paper · doi:10.48550/arxiv.1604.08378

Abstract

We prove convergence of a stochastic approximation of powers of the Riemann ζ function to a non-Gaussian multiplicative chaos measure, and prove that this measure is a non-trivial multifractal random measure. The results cover both the subcritical and critical chaos. A basic ingredient of the proof is a 'good' Gaussian approximation of the induced random fields that is potentially of independent interest.

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• On the limiting distribution of sums of random multiplicative functions

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