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On Probability Measures with Unbounded Angular Ratio

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Limit Theorems in Probability, Statistics and Number Theory

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 42))

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Abstract

The angular ratio is an important characteristic of probability measures on \(\mathbb{Z}\) in the theory of ergodic dynamical systems. Answering the J. Rosenblatt question, we describe probability measures whose spectrum is not inside some Stolz region at 1, i.e., which have unbounded angular ratio.

2010 Mathematics Subject Classification. Primary 37-XX, 60E10; secondary 60A10.

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References

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Acknowledgements

Research supported by SFB 701.

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Authors and Affiliations

  1. Fakultät für Mathematik, Universität Bielefeld, 100131, 33501, Bielefeld, Germany

    G. P. Chistyakov

Authors
  1. G. P. Chistyakov
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Correspondence to G. P. Chistyakov .

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Editors and Affiliations

  1. Mathematics Faculty, Ruhr-University Bochum, Universitätstr. 150, Bochum, 44780, Germany

    Peter Eichelsbacher

  2. Mathematics Faculty, University of Bielefeld, Universitätsstr. 25, Bielefeld, 33615, Germany

    Guido Elsner

  3. Mathematics Faculty, University of Bielefeld, Universitätsstr. 25, Bielefeld, 33615, Germany

    Holger Kösters

  4. Institute for Mathematical Statistics, University of Münster, Einsteinstrasse 62, Münster, 48149, Germany

    Matthias Löwe

  5. Mathematics Institute, University of München, Theresienstr. 39, München, 80333, Germany

    Franz Merkl

  6. Centre for Mathematics, Technische Universität München, Boltzmannstr. 3, Garching bei München, 85747, Germany

    Silke Rolles

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Dedicated to Friedrich Götze on the occasion of his sixtieth birthday

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Chistyakov, G.P. (2013). On Probability Measures with Unbounded Angular Ratio. In: Eichelsbacher, P., Elsner, G., Kösters, H., Löwe, M., Merkl, F., Rolles, S. (eds) Limit Theorems in Probability, Statistics and Number Theory. Springer Proceedings in Mathematics & Statistics, vol 42. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36068-8_5

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