The central limit theorem for random perturbations of rotations

Manfred Denker; Mikhail Gordin

doi:10.1007/s004400050160

The central limit theorem for random perturbations of rotations

Manfred Denker
, Mikhail Gordin

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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)
Pages (from-to)	1-16
Number of pages	16
Journal	Probability Theory and Related Fields
Volume	111
Issue number	1
DOIs	https://doi.org/10.1007/s004400050160
State	Published - May 1998

All Science Journal Classification (ASJC) codes

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

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title = "The central limit theorem for random perturbations of rotations",

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.",

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AU - Gordin, Mikhail

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N2 - 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.

AB - 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.

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JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

IS - 1

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The central limit theorem for random perturbations of rotations

Abstract

All Science Journal Classification (ASJC) codes

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