Mastrostefano, Daniele (2022) An almost sure upper bound for random multiplicative functions on integers with a large prime factor. Electronic Journal of Probability, 27 . doi:10.1214/22-EJP751 ISSN 1083-6489.

Preview

PDF WRAP-An-almost-sure-upper-bound-for-random-multiplicative-functions-on-integers-with-a-large-prime-factor-Mastrostefano-22.pdf - Published Version - Requires a PDF viewer. Available under License Creative Commons Attribution 4.0. Download (567Kb) | Preview

Request Changes to record.

Abstract

Let f be a Rademacher or a Steinhaus random multiplicative function. Let ε>0 small. We prove that, as x→+∞, we almost surely have

∣∑n≤xP(n)>√x f(n)∣≤√x(loglogx)1∕4+ε,

where P(n) stands for the largest prime factor of n. This gives an indication of the almost sure size of the largest fluctuations of f.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Iterative methods (Mathematics), Random variables , Probabilistic number theory
Journal or Publication Title:	Electronic Journal of Probability
Publisher:	University of Washington. Dept. of Mathematics
ISSN:	1083-6489
Official Date:	2022
Dates:	Date Event 2022 Published 2 March 2022 Available 31 January 2022 Accepted 10 June 2021 Submitted
Volume:	27
Number of Pages:	21
DOI:	10.1214/22-EJP751
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access (Creative Commons)
Date of first compliant deposit:	6 June 2022
Date of first compliant Open Access:	7 June 2022
RIOXX Funder/Project Grant:	Project/Grant ID RIOXX Funder Name Funder ID UNSPECIFIED [EPSRC] Engineering and Physical Sciences Research Council http://dx.doi.org/10.13039/501100000266

Request changes or add full text files to a record

Repository staff actions (login required)

View Item

Downloads