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arXiv · 1407.6065

A characterization of Benford's Law in discrete-time linear systems

Arno Berger·Gideon Eshun
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Abstract

A necessary and sufficient condition ("nonresonance") is established for every solution of an autonomous linear difference equation, or more generally for every sequence $(x^\top A^n y)$ with $x,y\in \mathbb{R}^d$ and $A\in \mathbb{R}^{d\times d}$, to be either trivial or else conform to a strong form of Benford's Law (logarithmic distribution of significands). This condition contains all pertinent results in the literature as special cases. Its number-theoretical implications are discussed in the context of specific examples, and so are its possible extensions and modifications.

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Arno Berger, Gideon Eshun. 2014-07-22. A characterization of Benford's Law in discrete-time linear systems. https://arxiv.org/abs/1407.6065

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