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arXiv · 1906.08573

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

Louis-Pierre Arguin·Lisa Hartung·Nicola Kistler
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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 [8], [2], and build on the convergence to 'Gaussian' multiplicative chaos proved in [14]. 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.

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Louis-Pierre Arguin, Lisa Hartung, Nicola Kistler. 2019-06-20. High points of a random model of the Riemann-zeta function and Gaussian multiplicative chaos. https://arxiv.org/abs/1906.08573

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