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On the limit distributions and asymptotics of extremal values for certain sequences of random variables

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References

  1. A. N. Livshits, “On a stationary sequence of random variables,” Preprint POMI P-5-92 (1992).

  2. J.-M. Dumont and A. Thomas, “Systèmes de numeration et fonctions fractales relatifs aux substitutions,”Theor. Comput. Sci.,65, No. 2, 153–168 (1989).

    MathSciNet  Google Scholar 

  3. J. Brillhart and P. Morton, “Über Summen von Rudin-Shapiroschen Koeffizienten,”Illinois J. Math.,22, 126–148 (1978).

    MathSciNet  Google Scholar 

  4. J. Brillhart, P. Erdős, and P. Morton, “On sums of Rudin-Shapiro coefficients, II,”Pacific J. Math.,107, No. 1, 39–70 (1983).

    MathSciNet  Google Scholar 

  5. B. Blackadar, “Symmetries of CAR-algebra,”Ann. Math.,131, No. 3, 589–623 (1990).

    MATH  MathSciNet  Google Scholar 

  6. D. Ruele,Statistical Mechanics: Rigorous Results, W. A. Benjamin (1974).

  7. Sh. Ito, “A construction of transversal flows for maximal Markov-automorphisms,” in:Second Japan-USSR Symposium on Probability Theory, Kyoto, Vol. 3 (1972), pp. 12–18.

  8. V. M. Alekseev and M. V. Yakobson, “Symbolic dynamics and hyperbolic dynamical systems,” Moscow (1979).

  9. J. G. Kemeny and J. L. Snell,Finite Markov Chains, Van Nostrand (1960).

  10. A. N. Livshits, “A way of proving topological mixing for a class of substitution,” Preprint POMI, P-10-91 (1991).

  11. R. S. Stricharts, “Self-similar measures and their transforms. III,”Indiana Univ. Math. J.,23, No. 2 367–413 (1993).

    Google Scholar 

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Authors
  1. A. N. Livshits
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Additional information

The limit distributions are studied for some sequences of sums of coordinate random variables over the dynamical system, connected with the Rudin-Shapiro substitution. The description of the limit distributions is presented on the basis of the expression for the sums of Rudin-Shapiro coefficients obtained earlier. The expression of the density is given for particular subsequences and the Markov representation for the “stationary” situation. The evaluation of the excess is given for a wide class of substitutions. Bibliography: 11 titles.

Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 216, 1994, pp. 86–103.

Translated by the author and V. Sudakov.

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Livshits, A.N. On the limit distributions and asymptotics of extremal values for certain sequences of random variables. J Math Sci 88, 59–71 (1998). https://doi.org/10.1007/BF02363263

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  • DOI: https://doi.org/10.1007/BF02363263

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