13 research outputs found
A Tauberian theorem for Ingham summation method
The aim of this work is to prove a Tauberian theorem for the Ingham
summability method. The Tauberian theorem we prove is then applied to analyze
asymptotics of mean values of multiplicative functions on natural numbers.Comment: 25 page
Voronoi summation formulae and multiplicative functions on permutations
We prove a Tauberian theorem for the Voronoi summation method of divergent
series with an estimate of the remainder term. The results on the Voronoi
summability are then applied to analyze the mean values of multiplicative
functions on random permutations.Comment: 43 pages. This paper is based on the material presented in chapters
1.1 and 1.2 of author's doctorial dissertation that was written and defended
at Vilnius University in 2004 under supervision of prof. E. Manstaviciu
Analysis of an exhaustive search algorithm in random graphs and the n^{c\log n} -asymptotics
We analyze the cost used by a naive exhaustive search algorithm for finding a
maximum independent set in random graphs under the usual G_{n,p} -model where
each possible edge appears independently with the same probability p. The
expected cost turns out to be of the less common asymptotic order n^{c\log n},
which we explore from several different perspectives. Also we collect many
instances where such an order appears, from algorithmics to analysis, from
probability to algebra. The limiting distribution of the cost required by the
algorithm under a purely idealized random model is proved to be normal. The
approach we develop is of some generality and is amenable for other graph
algorithms.Comment: 35 page
An analytic approach to the asymptotic variance of trie statistics and related structures
We develop analytic tools for the asymptotics of general trie statistics,
which are particularly advantageous for clarifying the asymptotic variance.
Many concrete examples are discussed for which new Fourier expansions are
given. The tools are also useful for other splitting processes with an
underlying binomial distribution. We specially highlight Philippe Flajolet's
contribution in the analysis of these random structures.Comment: 51 pages, the expressions of all Fourier coefficients are largely
simplified in this versio