English

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

Probability 2016-04-29 v1 Number Theory

Abstract

We prove convergence of a stochastic approximation of powers of the Riemann ζ\zeta 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.

Keywords

Cite

@article{arxiv.1604.08378,
  title  = {Multiplicative chaos measures for a random model of the Riemann zeta function},
  author = {Eero Saksman and Christian Webb},
  journal= {arXiv preprint arXiv:1604.08378},
  year   = {2016}
}