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

Abstract

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

References in corpus (6)

• Glass transition of a particle in a random potential, front selection in nonlinear RG and entropic phenomena in Liouville and SinhGordon models
• Critical Gaussian multiplicative chaos: Convergence of the derivative martingale
• Convergence of the centered maximum of log-correlated Gaussian fields
• The uniqueness of the Gaussian multiplicative chaos revisited
• Liouville Quantum Gravity on the Riemann sphere
• Glassy phase and freezing of log-correlated Gaussian potentials

Cited by in corpus (3)

• Moments of the Riemann zeta function on short intervals of the critical line
• Critical Gaussian multiplicative chaos: a review
• Maxima of branching random walks with piecewise constant variance