Empirical study of stochasticity for deterministic chaotical dynamics of geometric progressions of residues
type: Item
instance of: scholarly article
title: Empirical study of stochasticity for deterministic chaotical dynamics of geometric progressions of residues
zbMATH Open document ID: 1184.37011
author: Vładimir I. Arnold
published in: Functional Analysis and Other Mathematics
publication date: 2009-11-02T00:00:00Z
review text: \textit{A. Kolmogorov} discovered [Giorn. Ist. Ital. Atturi 4, 83-91 (1933; Zbl 0006.17402)] that the empirical statistics of several independent values of any random variable differs from the true distribution function of this variable in some universal way. The author uses this asymptotic Kolmogorov distribution, to test numerically the randomness of some examples of deterministic sequences (actually their first 50 terms), of arithmetic nature. He conjectures thus the ``non-randomness'' of arithmetic progressions, and the ``pseudo-randomness'' of Fibonacci numbers.
reviewed by: Jacques Franchi
Mathematics Subject Classification ID: 37A45
Mathematics Subject Classification ID: 37A50
Mathematics Subject Classification ID: 11K45
zbMATH DE Number: 5624150
zbMATH Keywords: pseudorandom numbers
zbMATH Keywords: residues of the division operation
zbMATH Keywords: random processes
zbMATH Keywords: independence
zbMATH Keywords: uniform distribution
MaRDI profile type: Publication
full work available at URL: s11853-009-0034-7
OpenAlex ID: W2045988212
DOI: 10.1007/S11853-009-0034-7
description: scientific article; zbMATH DE number 5624150