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

Autor:	Louis-Pierre Arguin, Lisa Hartung, Nicola Kistler
Jazyk:	angličtina
Rok vydání:	2019
Předmět:	Statistics and Probability 60J80 60G70 82B44 Applied Mathematics Modeling and Simulation Probability (math.PR) FOS: Mathematics Mathematics - Probability
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. 13 pages; missing sentence has been added to the arXiv abstract, pdf file has not changed
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a3a575f92f8b20664098465f306492d8 http://arxiv.org/abs/1906.08573 Zobrazit plný text záznamu