Papers by Eugenijus Manstavičius
Lietuvos matematikos rinkinys, Dec 19, 2002
Lietuvos matematikos rinkinys, Dec 21, 2003
Pusgrupi u adityvi uj u funkcij u reikšmi u koncentracija E. Manstavičius Nagrinėjama adityvi uj ... more Pusgrupi u adityvi uj u funkcij u reikšmi u koncentracija E. Manstavičius Nagrinėjama adityvi uj u funkcij u, apibrėžt u aritmetiniuose pusgrupiuose, reikšmi u koncentracija. Levy koncentracijos funkcijai irodytas Kolmogorovo-Rogozino nelygybės analogas.
A subset of cycles comprising a permutation σ in the symmetric group Sn, n ∈ N, is called a divis... more A subset of cycles comprising a permutation σ in the symmetric group Sn, n ∈ N, is called a divisor of σ. Then the partial sums over divisors with sizes up to un, 0 u 1, of values of a nonnegative multiplicative function on a random permutation define a stochastic process with nondecreasing trajectories. When normalized the latter is just a random distribution function supported by the unit interval. We establish that its expectations under various weighted probability measures defined on the subsets of Sn are quasihypergeometric distribution functions. Their limits as n → ∞ cover the class of two-parameter beta distributions. It is shown that, under appropriate conditions, the convergence rate is of the negative power of n order. That opens a new possibility to model the beta distributions using divisors of permutations.
Probabilistic number theory
Lithuanian Mathematical Journal, Jul 1, 1980
Sums of multiplicative functions and limit theorems in probabilistic number theory. II
Lithuanian Mathematical Journal, Apr 1, 1982
ABSTRACT
arXiv (Cornell University), May 13, 2016
An inequality for the variance of an additive function defined on random decomposable structures,... more An inequality for the variance of an additive function defined on random decomposable structures, called assemblies, is established. The result generalizes estimates obtained earlier in the cases of permutations and mappings of a finite set into itself. It is analogous to the Turán-Kubilius inequality for additive number-theoretic functions.
Analytic and probabilistic methods in number theory : proceedings of the Third International Conference in honour of J. Kubilius, Palanga, Lithuania, 24-28 September 2001 = Analiziniai ir tikimybiniai metodai skaičių teorijoje : trečiosios tarptautinés konferencijos J. Kubiliaus garbei darbų rink...
Litovskij matematičeskij sbornik, Jan 15, 1972
Α Tauber theorem and multiplicative functions on permutations
De Gruyter eBooks, Dec 31, 1999
Publicationes Mathematicae Debrecen, Jul 1, 1994
This work was done while the second author held a visiting professorship at the Paderborn Univers... more This work was done while the second author held a visiting professorship at the Paderborn Universität supported by the Deutsche Forschungsgemeinschaft.
Low of the iterated logarithm in the strassen formulation and additive functions
Lithuanian Mathematical Journal, 1986
Lithuanian Mathematical Journal, 1972
The abstracts (in two languages) can be found in the pdf file of the article. Original author nam... more The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: Э. Манставичюс. Асимптотическое разложение законов распределения мультипликативных арифметических функций E. Manstavičius. Aritmetinių multiplikatyvinių funkcijų pasiskirstymo dėsnių asimptotinis išdėstymas
The law of large numbers with respect to Ewens probability
Limit theorems for random permutations
Lithuanian Mathematical Journal, 1985
Functional limit theorems in theM-scheme
Lithuanian Mathematical Journal, 1997
Electronic Notes in Discrete Mathematics, 2017
We attempt to soften the conditions under which the component vector of a random decomposable str... more We attempt to soften the conditions under which the component vector of a random decomposable structure obeys the Poisson-Dirichlet distribution. The so-called Logarithmic Condition is relaxed to an averaged requirement. The results are focused on permutations sampled according to a generalized Ewens probability.
Summation of values of multiplicative functions on semigroups
Lithuanian Mathematical Journal, 1993
Lithuanian Mathematical Journal, 1984
Acta Mathematica Hungarica, 1995
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Papers by Eugenijus Manstavičius