We prove the existence of and describe limiting curves resulting from deviations in the partial sums in the ergodic theorem for cylinder functions and polynomial adic systems. For a general ergodic measure-preserving transformation and a summable function, we give a necessary condition for a limiting curve to exist. Our work generalizes results by É. Janvresse, T. de la Rue, and Y. Velenik and answers several questions from their work.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 448, 2016, pp. 177–200.
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Minabutdinov, A.R. Limiting Curves for Polynomial Adic Systems. J Math Sci 224, 286–303 (2017). https://doi.org/10.1007/s10958-017-3415-3
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DOI: https://doi.org/10.1007/s10958-017-3415-3