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Iterated Logarithm Laws and the Cycle Lengths of a Random Permutation

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Mathematics and Computer Science III

Part of the book series: Trends in Mathematics ((TM))

Abstract

We areconcerned with the iterated logarithm laws for mappings defined on thesymmetric group. For the sequences of the cycle lengthsand the different cyclelengths appearing in the decomposition of a random permutation,such laws provide asymptotical formulas valid uniformly in a wide region for the sequence parameter. The main results are analogues to Feller’s and Strassen’s theorems proved for partial sums of independent random variables.

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Author information

Authors and Affiliations

  1. Vilnius University, Department of Mathematics and Informatics, Vilnius, Lithuania

    Eugenijus Manstavičius

Authors
  1. Eugenijus Manstavičius
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Editor information

Editors and Affiliations

  1. Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstrasse 8-10, Wien, 1040, Austria

    Michael Drmota  & Bernhard Gittenberger  & 

  2. INRIA Rocquencourt, Le Chesnay, 78153, France

    Philippe Flajolet

  3. PRISM, Université de Versailles-St-Quentin, Bâtiment Descartes 45 avenue des Etats-Unis, Versailles Cedex, 78035, France

    Danièle Gardy

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Manstavičius, E. (2004). Iterated Logarithm Laws and the Cycle Lengths of a Random Permutation. In: Drmota, M., Flajolet, P., Gardy, D., Gittenberger, B. (eds) Mathematics and Computer Science III. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7915-6_5

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  • DOI: https://doi.org/10.1007/978-3-0348-7915-6_5

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9620-7

  • Online ISBN: 978-3-0348-7915-6

  • eBook Packages: Springer Book Archive

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