A stochastic process defined via the random permutation divisors

Fuente: arXiv
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Autor principal: Manstavičius, Eugenijus
Formato: Preprint
Publicado: 2025
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author Manstavičius, Eugenijus
author_facet Manstavičius, Eugenijus
contents The normalised partial sums of values of a nonnegative multiplicative function over divisors with appropriately restricted sizes of a random permutation from the symmetric group define trajectories of a stochastic process. We prove a functional limit theorem in the Skorokhod space when the permutations are drawn uniformly at random. Furthermore, we show that the paths of the limit process almost surely belong to the space of continuous functions on the unit interval and, exploiting the results from number-theoretical papers, we obtain rather complex formulas for the limits of joint power moments of the process.
format Preprint
id arxiv_https___arxiv_org_abs_2501_10096
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A stochastic process defined via the random permutation divisors
Manstavičius, Eugenijus
Probability
60F17, 60C05
The normalised partial sums of values of a nonnegative multiplicative function over divisors with appropriately restricted sizes of a random permutation from the symmetric group define trajectories of a stochastic process. We prove a functional limit theorem in the Skorokhod space when the permutations are drawn uniformly at random. Furthermore, we show that the paths of the limit process almost surely belong to the space of continuous functions on the unit interval and, exploiting the results from number-theoretical papers, we obtain rather complex formulas for the limits of joint power moments of the process.
title A stochastic process defined via the random permutation divisors
topic Probability
60F17, 60C05
url https://arxiv.org/abs/2501.10096