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The law of the iterated logarithm for random permutations

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References

  1. R. Arratia, A. D. Barbour, and S. Tavaré, Random combinatorial structures and prime factorizations,Notices Amer. Math. Soc.,44 (8), 903–910 (1997).

    MATH  MathSciNet  Google Scholar 

  2. R. Arratia and S. Tavaré, The cycle structure of random permutations,Ann. Probab. 20 (3), 1567–1591 (1992).

    MATH  MathSciNet  Google Scholar 

  3. J. M. DeLaurentis and B. G. Pittel, Random permutations and the Brownian motion,Pacific J. Math.,119 (2), 287–301 (1985).

    MATH  MathSciNet  Google Scholar 

  4. P. Erdös and P. Turán, On some problems of a statistical group theory. I,Z. Wahrsch. verw. Geb.,4, 175–186 (1965).

    Article  MATH  Google Scholar 

  5. V. L. Goncharov, On the distribution of cycles in permutations,Dokl. Akad. Nauk SSSR,35 (9), 299–301 (1942).

    Google Scholar 

  6. V. F. Kolchin,Random Mappings, Optimization Software, Inc., New York (1984).

    Google Scholar 

  7. J. Kubilius,Probabilistic Methods in the theory of Numbers, Amer. Math. Soc., Providence (1964).

    MATH  Google Scholar 

  8. E. Manstavičius, Strong convergence of additive arithmetic functions,Lith. Math. J.,25, 127–137 (1985).

    Google Scholar 

  9. E. Manstavičius, Law of the iterated logarithm in the Strassen formulation and additive functions,Lith. Math. J.,26, 50–56 (1986).

    Article  MATH  Google Scholar 

  10. E. Manstavičius, Laws of the iterated logarithm for additive functions,Colloq. Math. Soc. János Bolyai, Number Theory,51, 279–299 (1987).

    Google Scholar 

  11. E. Manstavičius, Additive and multiplicative functions on random permutations,Lith. Math. J.,36, 400–408 (1996).

    Article  MATH  Google Scholar 

  12. E. Manstavičius,The Berry-Esseen bound in the theory of random permutations, Preprint 96-12, Vilnius University (1996) (to appear inThe Ramanujan J.).

  13. V. V. Petrov,Sums of Independent Random Variables [in Russian], Nauka, Moscow (1972).

    Google Scholar 

  14. I. Z. Ruzsa, Generalized moments of additive functions,J. Number Theory,18, 27–33 (1984).

    Article  MATH  MathSciNet  Google Scholar 

  15. I. Z. Ruzsa, Effective results in probabilistic number theory, in:Théorie elémentaire et analytique des nombres, J. Coquet (Ed.), Dépt. Math. Univ. Valenciennes (1982), pp. 107–130.

  16. Q.-M. Shao, Strong approximation theorems for independent random variables and their applications,J. Multivariate Anal.,52, 107–130 (1995).

    Article  MATH  MathSciNet  Google Scholar 

  17. H. Teicher, On the law of the iterated logarithm,Ann. Probab.,2, 714–728 (1974).

    MATH  MathSciNet  Google Scholar 

  18. G. A. Watterson, The sampling theory of selectively neutral alleles,Adv. Appl. Probab.,6, 463–488 (1974).

    Article  MATH  MathSciNet  Google Scholar 

Download references

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Partially supported by the Lithuanian State Science and Studies Foundation.

Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 38, No. 2, pp. 205–220, April–June, 1998.

Translated by E. Manstavičius

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Manstavičius, E. The law of the iterated logarithm for random permutations. Lith Math J 38, 160–171 (1998). https://doi.org/10.1007/BF02465552

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  • DOI: https://doi.org/10.1007/BF02465552

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