Distribution of the sum-of-digits function of random integers: a survey

Louis H. Y. Chen; Hsien-Kuei Hwang; Vytas Zacharovas

doi:10.1214/12-ps213

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arXiv · 1212.6697

Distribution of the sum-of-digits function of random integers: a survey

Louis H. Y. Chen·Hsien-Kuei Hwang·Vytas Zacharovas

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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 and the Parseval identity. We also extend the study to a simple, general numeration system for which similar approximation theorems are derived.

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Louis H. Y. Chen, Hsien-Kuei Hwang, Vytas Zacharovas. 2012-12-30. Distribution of the sum-of-digits function of random integers: a survey. https://doi.org/10.1214/12-ps213

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