2000 character limit reached
Benford's law and the C$β$E (2302.02932v4)
Published 6 Feb 2023 in math.PR, math-ph, and math.MP
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.
Collections
Sign up for free to add this paper to one or more collections.
