Vytas Zacharovas

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Asymptotics of the variances of many cost measures in random digital search trees are often notoriously messy and involved to obtain. A new approach is proposed to facilitate such an analysis for several shape parameters on random symmetric digital search trees. Our approach starts from a more careful normalization at the level of Poisson generating(More)
Asymptotics of the variances of many cost measures in random digital search trees are often notoriously messy and involved to obtain. A new approach is proposed to facilitate such an analysis for several shape parameters on random symmetric digital search trees. Our approach starts from a more careful normalization at the level of Poisson generating(More)
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(More)
A family of measures on the set of permutations of the first n integers, known as Ewens sampling formula, arises in population genetics. In a series of papers, the first two authors have developed necessary and sufficient conditions for the weak convergence of a partial sum process based on these measures to a process with independent increments. Under very(More)
A new approach to Poisson approximation is proposed. The basic idea is very simple and based on properties of the Charlier polynomials and the Parseval identity. Such an approach quickly leads to new effective bounds for several Poisson approximation problems. A selected survey on diverse Poisson approximation results is also given. MSC 2000 Subject(More)
Abstract: We review some probabilistic properties of the sum-of-digits function of random integers. New asymptotic approximations to the total variation distance and its refinements are also derived. Four different approaches are used: a classical probability approach, Stein’s method, an analytic approach and a new approach based on Krawtchouk polynomials(More)
σ = κ1κ2...κω this decomposition is unique up to the order of the multiplicands. We will call a function f : Sn → C multiplicative if f(σ) = f(κ1)f(κ2)...f(κn). In what follows we will assume that the value of f on cycles depends only on the length of cycle, that is f(κ) = f̂(|κ|), where |κ| the order of cycle κ. Let mk(σ) be equal to the number of cycles(More)
We analyze the cost used by a naive exhaustive search algorithm for finding a maximum independent set in random graphs under the usual Gn;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 log , which we explore from several different perspectives. Also(More)