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

TL;DR

This paper introduces analytic tools for understanding the asymptotic variance of trie statistics, providing new Fourier expansions and insights applicable to related splitting processes with binomial distributions.

Contribution

It develops novel analytic methods for asymptotic analysis of trie statistics, emphasizing variance and Fourier expansions, extending to other splitting processes.

Findings

New Fourier expansions for trie statistics

Analytic tools clarify asymptotic variance

Applicable to binomial-based splitting processes

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.