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

Autor:	Arguin, Louis-Pierre, Hartung, Lisa, Kistler, Nicola
Rok vydání:	2019
Předmět:	Mathematics - Probability 60J80 60G70 82B44
Druh dokumentu:	Working Paper
Popis:	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. Comment: 13 pages; missing sentence has been added to the arXiv abstract, pdf file has not changed
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1906.08573 Zobrazit plný text záznamu View this record from Arxiv