Pith. sign in

REVIEW 1 cited by

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

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2302.02932 v4 pith:MHJYUB4Q submitted 2023-02-06 math.PR math-phmath.MP

Nedialko Bradinoff , Maurice Duits This is my paper · ORCID
classification math.PRmath-phmath.MP
keywords digitsabsolutebenfordbetacharacteristicpolynomialvaluebecome
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
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.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Moments of characteristic polynomials for classical $\beta$ ensembles

    math-ph 2025-02 accept novelty 6.0 of 10

    Even-power characteristic polynomial moments for Gaussian, Laguerre, and Jacobi beta ensembles are shown to have large-N expansions with explicit error bounds, a universal Barnes-G constant, and new formulas for weigh...

Pith tools