Asymptotic behaviors of convolution powers of the Riemann zeta distribution

TL;DR

This paper investigates the asymptotic behavior of convolution powers of the Riemann zeta distribution, a rare example of a discrete distribution with infinite support, expanding understanding of its probabilistic properties.

Contribution

It introduces the Riemann zeta distribution as a notable discrete distribution with infinite support and analyzes its convolution powers' asymptotic behaviors.

Findings

Identifies asymptotic patterns of convolution powers

Highlights properties of the Riemann zeta distribution

Contributes to the theory of discrete distributions with infinite support

Abstract

In probability theory, there exist discrete and continuous distributions. Generally speaking, we do not have sufficient kinds and properties of discrete ones compared to the continuous ones. In this paper, we treat the Riemann zeta distribution as a representative of few known discrete distributions with infinite supports. Some asymptotic behaviors of convolution powers of the Riemann zeta distribution are discussed.