### Abstract

We prove a functional central limit theorem for stationary random sequences given by the transformations T_{ε,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 language | English (US) |
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Pages (from-to) | 1-16 |

Number of pages | 16 |

Journal | Probability Theory and Related Fields |

Volume | 111 |

Issue number | 1 |

DOIs | |

State | Published - May 1998 |

### All Science Journal Classification (ASJC) codes

- Analysis
- Statistics and Probability
- Statistics, Probability and Uncertainty

## Fingerprint Dive into the research topics of 'The central limit theorem for random perturbations of rotations'. Together they form a unique fingerprint.

## Cite this

Denker, M., & Gordin, M. (1998). The central limit theorem for random perturbations of rotations.

*Probability Theory and Related Fields*,*111*(1), 1-16. https://doi.org/10.1007/s004400050160