A theorem about uniform distribution

Yakov Sinai

Research output: Contribution to journalArticlepeer-review


Many problems of combinatorial number theory can be formulated in terms of behavior of orbits of certain transformations acting on the spaces of integers or their subsets. Their analysis can be reduced to problems embracing number theory, probability theory and dynamical systems. In this paper we consider one such question originated from the famous (3x + 1)-problem, which illustrates the difficulties which sometimes arise. The main theorem gives the limiting uniform distribution of certain functionals of independent random variables.

Original languageEnglish (US)
Pages (from-to)581-588
Number of pages8
JournalCommunications In Mathematical Physics
Issue number1-3
StatePublished - Dec 2004

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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