On some questions of V.I. Arnold on the stochasticity of geometric and arithmetic progressions

TL;DR

This paper explores V.I. Arnold's questions on the pseudorandomness of deterministic sequences, analyzing their stochasticity through probability and number theory to address open questions he posed.

Contribution

It provides a detailed analysis of Arnold's questions on stochasticity, connecting probability theory and number theory to advance understanding of pseudorandomness in sequences.

Findings

Clarified the probabilistic background of Arnold's stochasticity parameter

Provided answers to specific questions raised by Arnold

Enhanced understanding of pseudorandomness in deterministic sequences

Abstract

In some of his final papers, V.I. Arnold studied pseudorandomness properties of finite deterministic sequences, which he measured in terms of their "stochasticity parameter". In the present paper we illustrate the background in probability theory and number theory of some of his considerations, and give answers to some of the questions raised in his papers.