| Title:
|
Discrete limit laws for additive functions on the symmetric group (English) |
| Author:
|
Manstavičius, Eugenijus |
| Language:
|
English |
| Journal:
|
Acta Mathematica Universitatis Ostraviensis |
| ISSN:
|
1214-8148 |
| Volume:
|
13 |
| Issue:
|
1 |
| Year:
|
2005 |
| Pages:
|
47-55 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Inspired by probabilistic number theory, we establish necessary and sufficient conditions under which the numbers of cycles with lengths in arbitrary sets posses an asymptotic limit law. The approach can be extended to deal with the counts of components with the size constraints for other random combinatorial structures. (English) |
| Keyword:
|
random permutation |
| Keyword:
|
cycle structure |
| Keyword:
|
Poisson distribution |
| Keyword:
|
factorial moment |
| MSC:
|
05A16 |
| MSC:
|
05D40 |
| MSC:
|
60C05 |
| idZBL:
|
Zbl 1200.60012 |
| idMR:
|
MR2290418 |
| . |
| Date available:
|
2009-12-29T09:17:13Z |
| Last updated:
|
2015-03-15 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/137471 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[8] Manstavičius E.: Additive and multiplicative functions on random permutations., Lith. Math. J. 36(1996), 4, 400–408. MR 1456921, 10.1007/BF02986863 |
| Reference:
|
[9] Manstavičius E.: The law of iterated logarithm for random permutations., Lith. Math. J. 38(1998), 2, 160–171. MR 1657912, 10.1007/BF02465552 |
| Reference:
|
[10] Manstavičius E.: Functional limit theorem for sequences of mappings on the symmetric group., In: Anal. Probab. Methods in Number Theory, A. Dubickas et al (Eds), TEV, Vilnius, 2002, 175–187. MR 1964861 |
| Reference:
|
[11] Manstavičius E.: Value concentration of additive functions on random permutations., Acta Applicandae Math. 79(2003), 1–8. MR 2021871, 10.1023/A:1025812604540 |
| Reference:
|
[12] Manstavičius E.: Asymptotic value distribution of additive functions defined on the symmetric group., (submitted, 2005, 23 p.). |
| Reference:
|
[13] Šiaulys J.: Factorial moments for distributions of additive functions., Lith. Math. J. 40(2000), 4, 389–408. 10.1023/A:1007617714857 |
| . |
