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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)

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 consider sequences of random variables whose probability generating functions have only roots on the unit circle, which has only been sporadically studied in the literature. We show that the random variables are asymptotically normally distributed if and only if the fourth central and normalized (by the standard deviation) moment tends to 3, in contrast… (More)

- Louis H Y Chen, Hsien-Kuei Hwang, Vytas Zacharovas, L H Y Chen
- 2014

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 and the… (More)

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.… (More)

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