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'ss Law and the further digits converge to a uniform distribution. Key to our proofs is a bound on the rate of convergence in total variation norm in the CLT for the logarithm of the characteristic polynomial.
Benford’s law and the CβE / Bradinoff, N., Duits, M.. - In: RANDOM MATRICES: THEORY AND APPLICATIONS. - ISSN 2010-3263. - (2025). [10.1142/S2010326325500017]
Benford’s law and the CβE
Maurice DuitsCo-primo
Membro del Collaboration Group
2025
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'ss Law and the further digits converge to a uniform distribution. Key to our proofs is a bound on the rate of convergence in total variation norm in the CLT for the logarithm of the characteristic polynomial.File allegati a questo prodotto
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