An analytic approach to the asymptotic variance of trie statistics and related structures

Michael Fuchs; Hsien-Kuei Hwang; Vytas Zacharovas

An analytic approach to the asymptotic variance of trie statistics and related structures

Combinatorics 2013-04-17 v3 Data Structures and Algorithms

Authors: Michael Fuchs , Hsien-Kuei Hwang , Vytas Zacharovas

Abstract

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.

Keywords

trie statistics asymptotic variance analytic combinatorics Fourier expansions splitting processes binomial distribution

Cite

@article{arxiv.1303.4244,
  title  = {An analytic approach to the asymptotic variance of trie statistics and related structures},
  author = {Michael Fuchs and Hsien-Kuei Hwang and Vytas Zacharovas},
  journal= {arXiv preprint arXiv:1303.4244},
  year   = {2013}
}

Comments

51 pages, the expressions of all Fourier coefficients are largely simplified in this version

An analytic approach to the asymptotic variance of trie statistics and related structures

Abstract

Keywords

Cite

Comments

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