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Proving Randomness

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Probabilistic Diophantine Approximation

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Abstract

In Sect. 1.5 we almost proved Theorem 1.2 in the special case of the golden ratio. The missing part was the variance, but we took care of this particular issue in Sect. 3.2. The golden ratio has the simplest continued fraction among all quadratic irrationals, and this extreme simplicity (the length of the period is one, and every partial quotient is one) is rather misleading.

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  1. Department of Mathematics, Rutgers University, Piscataway, NJ, USA

    József Beck

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Beck, J. (2014). Proving Randomness. In: Probabilistic Diophantine Approximation. Springer Monographs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-10741-7_4

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