Ergodic and statistical properties of b-free numbers

M. Avdeeva, F. Cellarosi, Ya G. Sinai

Research output: Contribution to journalArticle

Abstract

In this survey, we outline several results on the distribution of B-free integers and explore a random process naturally associated to them. We show how, notwithstanding the rigid ergodic properties of this process (zero entropy, pure point spectrum, no weak mixing), it exhibits a central limit theorem resembling a theorem by Beck on the circle rotation by a quadratic surd. We explain the connection of the random process to the distribution of B-free integers in short intervals, with particular emphasis on their variance and higher moments.

Original languageEnglish (US)
Pages (from-to)569-589
Number of pages21
JournalTheory of Probability and its Applications
Volume61
Issue number4
DOIs
StatePublished - Jan 1 2017

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • B-free integers
  • Central limit theorem
  • Correlation functions
  • Entropy
  • Möbius function

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