Electronic Journal of Probability

A Central Limit Theorem for Random Ordered Factorizations of Integers

Hsien-Kuei Hwang and Svante Janson

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Write an integer as finite products of ordered factors belonging to a given subset $\mathcal{P}$ of integers larger than one. A very general central limit theorem is derived for the number of ordered factors in random factorizations for any subset $\mathcal{P}$ containing at least two elements. The method of proof is very simple and relies in part on Delange’s Tauberian theorems and an interesting Tauberian technique for handling Dirichlet series associated with odd centered moments.

An erratum is available in EJP volume 18 paper 16

Article information

Electron. J. Probab. Volume 16 (2011), paper no. 12, 347-361.

Accepted: 16 February 2011
First available in Project Euclid: 1 June 2016

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Mathematical Reviews number (MathSciNet)

Primary: 11N80: Generalized primes and integers
Secondary: 11N37: Asymptotic results on arithmetic functions 11K65: Arithmetic functions [See also 11Nxx] 11N60: Distribution functions associated with additive and positive multiplicative functions 11M45: Tauberian theorems [See also 40E05] 60F05: Central limit and other weak theorems

Tauberian theorems asymptotic normality ordered factorizations method of moments Dirichlet series

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Hwang, Hsien-Kuei; Janson, Svante. A Central Limit Theorem for Random Ordered Factorizations of Integers. Electron. J. Probab. 16 (2011), paper no. 12, 347--361. doi:10.1214/EJP.v16-858. http://projecteuclid.org/euclid.ejp/1464820181.

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