On permutation-invariance of limit theorems

Research output: Contribution to journalArticlepeer-review


By a classical principle of probability theory, sufficiently thin subsequences of general sequences of random variables behave like i.i.d. sequences. This observation not only explains the remarkable properties of lacunary trigonometric series, but also provides a powerful tool in many areas of analysis, such as the theory of orthogonal series and Banach space theory. In contrast to i.i.d. sequences, however, the probabilistic structure of lacunary sequences is not permutation-invariant and the analytic properties of such sequences can change after rearrangement. In a previous paper we showed that permutation-invariance of subsequences of the trigonometric system and related function systems is connected with Diophantine properties of the index sequence. In this paper we will study permutation-invariance of subsequences of general r.v. sequences.
Original languageEnglish
Pages (from-to)372–379
JournalJournal of Complexity
Issue number3
Early online dateJun 2014
Publication statusPublished - Jun 2015

Fields of Expertise

  • Information, Communication & Computing

Treatment code (Nähere Zuordnung)

  • Basic - Fundamental (Grundlagenforschung)


Dive into the research topics of 'On permutation-invariance of limit theorems'. Together they form a unique fingerprint.

Cite this