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

## TL;DR

This paper investigates the behavior of high points in a random model of the Riemann-zeta function, demonstrating convergence of their total mass to Gaussian multiplicative chaos using probabilistic methods.

## Contribution

It establishes the almost sure convergence of the total mass of high points to Gaussian multiplicative chaos in a specific random model of the Riemann-zeta function.

## Key findings

- Total mass of high points converges to Gaussian multiplicative chaos
- Almost sure convergence established using second moment method
- Branching approximation aids in the proof

## 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.