Benford's law and the C$\beta$E

Nedialko Bradinoff; Maurice Duits

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arXiv · 2302.02932

Benford's law and the C$\beta$E

Nedialko Bradinoff·Maurice Duits

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Abstract

We study the individual digits for the absolute value of the characteristic polynomial for the Circular $\beta$-Ensemble. We show that, in the large $N$ limit, the first digits obey Benford's Law and the further digits become uniformly distributed. Key to the proofs is a bound on the rate of convergence in total variation norm in the CLT for the logarithm of the absolute value of the characteristic polynomial.

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Nedialko Bradinoff, Maurice Duits. 2023-02-06. Benford's law and the C$\beta$E. https://arxiv.org/abs/2302.02932

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