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Bradinoff, N and Duits, M (2023)

Benford's law and the CβE

Preprint arXiv:2302.02932 [math.PR]; last accessed March 10, 2023.

ISSN/ISBN: Not available at this time. DOI: 10.48550/ARXIV.2302.02932

Abstract: We study the individual digits for the absolute value of the characteristic polynomial for the Circular β-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.

@misc{, doi = {10.48550/ARXIV.2302.02932}, url = {}, author = {Bradinoff, Nedialko and Duits, Maurice}, title = {Benford's law and the C$β$E}, publisher = {arXiv}, year = {2023}, copyright = {Creative Commons Attribution 4.0 International}, }

Reference Type: Preprint

Subject Area(s): Probability Theory