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Zapiski Nauchnykh Seminarov POMI, 1997, Volume 240, Pages 78–81
(Mi znsl467)
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This article is cited in 1 scientific paper (total in 1 paper)
Asymptotically Gaussian distribution for random perturbations of rotations of the circle
M. I. Gordina, M. Denkerb a St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
b Institute for Mathematical Stochastics, Georg-August-Universität Göttingen
Abstract:
Let $T_{\epsilon,\omega}$ be a self-map of the two dimensional torus $\mathbb T^2$ given by the formula
$T_{\epsilon,\omega}\colon(x,y)\to(2x,y+\omega+\epsilon x)\bmod1$. If $\epsilon$ is an irrational number, a version of the functional central limit theorem is formulated for variables of the form $n^{-1/2} \sum_{k=0}^{\infty}f \circ T^k_{\epsilon,\omega}$ where $f$ is a member of a class of real valued functions on $\mathbb T^2$ described in terms of $\epsilon$. The proof will be published elsewhere.
Received: 19.09.1996
Citation:
M. I. Gordin, M. Denker, “Asymptotically Gaussian distribution for random perturbations of rotations of the circle”, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part II, Zap. Nauchn. Sem. POMI, 240, POMI, St. Petersburg, 1997, 78–81; J. Math. Sci. (New York), 96:5 (1999), 3493–3495
Linking options:
https://www.mathnet.ru/eng/znsl467 https://www.mathnet.ru/eng/znsl/v240/p78
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