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A basic theory of Benford’s law. (English) Zbl 1245.60016
Summary: Drawing from a large, diverse body of work, this survey presents a comprehensive and unified introduction to the mathematics underlying the prevalent logarithmic distribution of significant digits and significands, often referred to as Benford’s law (BL) or, in a special case, as the first digit law. The invariance properties that characterize BL are developed in detail. Special attention is given to the emergence of BL in a wide variety of deterministic and random processes. Though mainly expository in nature, the article also provides strengthened versions of and simplified proofs for many key results in the literature. Numerous intriguing problems for future research arise naturally.
Reviewer: Reviewer (Berlin)

MSC:
60E05 Probability distributions: general theory
60-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory
11K06 General theory of distribution modulo \(1\)
39A60 Applications of difference equations
37A45 Relations of ergodic theory with number theory and harmonic analysis (MSC2010)
60F15 Strong limit theorems
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References:
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