| Title |
Effective variance estimates of additive functions defined on random combinatorial objects |
| Translation of Title |
Efektyvūs dispersijų įverčiai adityviosioms funkcijoms, apibrėžtoms virš atsitiktinių kombinatorinių objektų. |
| Authors |
Karbonskis, Arvydas |
| DOI |
10.15388/vu.thesis.956 |
| Full Text |
|
| Pages |
92 |
| Keywords [eng] |
random permutation ; weighted multiset ; variance estimate ; eigenvalue ; additive function |
| Abstract [eng] |
The dissertation investigates variance estimates for additive functions defined on random permutations and weighted multisets. It extends classical ideas of probabilistic number theory associated with the Turán–Kubilius inequality to random combinatorial structures. For permutations, sharp upper and lower variance bounds for strongly additive functions are obtained together with refined remainder estimates; the constants 3/2 and 2/3 appearing in these bounds are shown to be optimal. For weighted multisets, analogous results are obtained for completely additive functions. |
| Dissertation Institution |
Vilniaus universitetas. |
| Type |
Doctoral thesis |
| Language |
English |
| Publication date |
2026 |
