A Characterization of Benford’s Law in Discrete-Time Linear Systems

@article{Berger2014ACO,
  title={A Characterization of Benford’s Law in Discrete-Time Linear Systems},
  author={Arno Berger and Gideon Eshun},
  journal={Journal of Dynamics and Differential Equations},
  year={2014},
  volume={28},
  pages={431-469}
}
A necessary and sufficient condition (“nonresonance”) is established for every solution of an autonomous linear difference equation, or more generally for every sequence $$(x^\top A^n y)$$(x⊤Any) with $$x,y\in \mathbb {R}^d$$x,y∈Rd and $$A\in \mathbb {R}^{d\times d}$$A∈Rd×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… CONTINUE READING

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