×

The law of iterated logarithm for logarithmic combinatorial assemblies. (English) Zbl 1132.05006

Lith. Math. J. 46, No. 4, 432-445 (2006); and Liet. Mat. Rink. 46, No. 4, 532-547 (2006).
Summary: The strong convergence of dependent random variables is analyzed and the law of iterated logarithm for real additive functions defined on the class \(\mathcal{A}_n\) of combinatorial assemblies is obtained.

MSC:

05A18 Partitions of sets
60C05 Combinatorial probability
Full Text: DOI

References:

[1] R. Arratia, A. D. Barbour, and S. Tavaré, Logarithmic Combinatorial Structures: a Probabilistic Approach, EMS Monographs in Math., The EMS Publishing House, Zürich (2003). · Zbl 1040.60001
[2] G. J. Babu and E. Manstavičius, Brownian motion for random permutations, Sankhyā Ser. A, 61(3), 312–327 (1999). · Zbl 0978.60027
[3] G. J. Babu and E. Manstavičius, Limit process with independent increments for the Ewens sampling formula, Ann. Inst. Statist. Math., 54(3), 607–620 (2002). · Zbl 1014.92024 · doi:10.1023/A:1022419328971
[4] V. L. Goncharov, On the distribution of cycles in permutations, Dokl. AN SSRS, 35, 299–301 (1942). · Zbl 0063.01683
[5] H.-K. Hwang, Asymptotic of Poisson approximation of random discrete distributions, Adv. Appl. Probab, 31, 448–491 (1999). · Zbl 0945.60001 · doi:10.1239/aap/1029955143
[6] P. Erdos and P. Turán, On some problems of statistical group theory, I, Z. Wahrsch. verw. Geb., 4, 175–186 (1965). · Zbl 0137.25602 · doi:10.1007/BF00536750
[7] V. F. Kolchin, B. A. Sevastyanov, and V. P. Chistyakov, Random Allocations, Halsted Press, Washington (1978).
[8] V. F. Kolchin, Random Mappings, Optimization Software, Inc., New York (1986).
[9] E. Manstavičius, Laws of the iterated logarithm for additive functions, Colloq. Math. Soc. János Bolyai, Number Theory, 51, 279–299 (1987).
[10] E. Manstavičius, Additive and multiplicative functions on random permutations, Lith. Math. J., 36(4), 400–408 (1996). · Zbl 0899.11040 · doi:10.1007/BF02986863
[11] E. Manstavičius, The law of iterated logarithm for random permutations, Lith. Math. J., 38, 160–171 (1998). · Zbl 0930.60015 · doi:10.1007/BF02465552
[12] E. Manstavičius, Iterated logarithm laws and the cycle lengths of a random permutation, in: Trends in Mathematics, Mathematics and Computer Science III, Algorithms, Trees, Combinatorics and Probabilities, M. Drmota et al. (Eds.), Birkhauser, Basel (2004), pp. 39–47.
[13] V. V. Petrov, Sums of Independent Random Variables (in Russian), Nauka, Moscow (1972). · Zbl 0288.60050
[14] L. A. Shepp and S. P. Lloyd, Ordered cycle lengths in a random permutation, Trans. Amer. Math. Soc., 121, 340–357 (1966). · Zbl 0156.18705 · doi:10.1090/S0002-9947-1966-0195117-8
[15] D. Stark, Total variation asymptotics for refined Poisson process approximations of logarithmic combinatorial assemblies, Combin. Probab. Comput., 8, 567–598 (1999). · Zbl 0960.60015 · doi:10.1017/S0963548399004009
[16] H. Teicher, On the law of iterated logarithm, Ann. Probab., 4, 714–728 (1974). · Zbl 0286.60013 · doi:10.1214/aop/1176996614
[17] V. Zacharovas, The convergence rate to the normal law of a certain variable defined on random polynomials, Lith. Math. J., 42(1), 88–107 (2002). · Zbl 1015.60021 · doi:10.1023/A:1015077919456
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.