High points of a random model of the Riemann-zeta function and Gaussian multiplicative chaos

Louis-Pierre Arguin, Lisa Hartung and Nicola Kistler

Stochastic Processes and their Applications, 2022, vol. 151, issue C, 174-190

Abstract: We study the total mass of high points in a random model for the Riemann-zeta function. We consider the same model as in Harper (2013) and Arguin et al. (2017), and build on the convergence to Gaussian multiplicative chaos proved in Saksman and Webb (2016). We show that the total mass of points which are a linear order below the maximum, divided by their expectation, converges almost surely to the Gaussian multiplicative chaos of the approximating Gaussian process times a random function. We use the second moment method together with a branching approximation to establish this convergence.

Keywords: Riemann-Zeta function; High points; Gaussian multiplicative chaos; Extreme values (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2022.04.017

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