Geodesic
Laws of large numbers and the central limit theorem for sequences of coefficients of rotational expansions
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part I, Tome 223 (1995), pp. 313-322

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For rotational expansions introduced in [1], conditions under which the law of large numbers, the strong law of large numbers, or the central limit theorem hold for Markov sequences of coefficients, are found. Answers are given in terms of the rate of growth of the quotients $a_n$. Bibliography: 8 titles. 
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     author = {N. A. Sidorov},
     title = {Laws of large numbers and the central limit theorem for sequences of coefficients of rotational expansions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {313--322},
     publisher = {mathdoc},
     volume = {223},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1995_223_a16/}
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N. A. Sidorov. Laws of large numbers and the central limit theorem for sequences of coefficients of rotational expansions. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part I, Tome 223 (1995), pp. 313-322. http://geodesic.mathdoc.fr/item/ZNSL_1995_223_a16/