The central limit theorem for random perturbations of rotations

Manfred Denker, Mikhail Gordin

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

We prove a functional central limit theorem for stationary random sequences given by the transformations Tε,ω(x,y) = (2x,y + ω + εx) mod 1 on the two-dimensional torus. This result is based on a functional central limit theorem for ergodic stationary martingale differences with values in a separable Hilbert space of square integrable functions.

Original languageEnglish (US)
Pages (from-to)1-16
Number of pages16
JournalProbability Theory and Related Fields
Volume111
Issue number1
DOIs
StatePublished - May 1998

All Science Journal Classification (ASJC) codes

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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