On the discrepancy of powers of random variables

Nicolas Chenavier; Dominique Schneider

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arXiv · 1705.04626

On the discrepancy of powers of random variables

Nicolas Chenavier·Dominique Schneider

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Abstract

Let $(d_n)$ be a sequence of positive numbers and let $(X_n)$ be a sequence of positive independent random variables. We provide an upper bound for the deviation between the distribution of the mantissaes of $(X_n^{d_n})$ and the Benford's law. If $d_n$ goes to infinity at a rate at most polynomial, this deviation converges a.s. to 0 as $N$ goes to infinity.

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Nicolas Chenavier, Dominique Schneider. 2017-05-12. On the discrepancy of powers of random variables. https://arxiv.org/abs/1705.04626

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