Benford's law and the C$\beta$E
Probability
2023-12-19 v4 Mathematical Physics
math.MP
Abstract
We study the individual digits for the absolute value of the characteristic polynomial for the Circular -Ensemble. We show that, in the large 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.
Cite
@article{arxiv.2302.02932,
title = {Benford's law and the C$\beta$E},
author = {Nedialko Bradinoff and Maurice Duits},
journal= {arXiv preprint arXiv:2302.02932},
year = {2023}
}
Comments
28 pages, references added, parts are rewritten, Theorem 1.3 added