Affiliation:
1. University of Alberta , Edmonton , Canada
Abstract
Abstract
For sequences sufficiently close to (a log n), with an arbitrary real constant a, this note describes the precise asymptotics of the associated empirical distributions modulo one, with respect to the Kantorovich metric as well as a discrepancy-style metric. In particular, the note demonstrates how these asymptotics depend on a in a delicate, discontinuous way. The results strengthen and complement known facts in the literature.
Subject
General Earth and Planetary Sciences,General Environmental Science
Reference26 articles.
1. [1] BECK, J.: Randomness of the square root of 2 and the giant leap, Part 1,Period. Math. Hungar. 60 (2010), 137–242.10.1007/s10998-010-2137-9
2. [2] BERGER, A.: Circling the uniform distribution (in preparation).
3. [3] BERGER, A.—HILL, T. P.: An Introduction to Benford’s Law. Princeton University Press, Princeton, NJ, 2015.
4. [4] BROWN, L.—STEINERBERGER, S.: On the Wasserstein distance between classical sequences and the Lebesgue measure, Trans. Amer. Math. Soc. 373 (2020), 8943–8962.10.1090/tran/8212
5. [5] BURTON, R.—DENKER, M.: On the central limit theorem for dynamical systems,Trans. Amer. Math. Soc. 302 (1987), 715–726.10.1090/S0002-9947-1987-0891642-6
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Circling the uniform distribution;Journal of Mathematical Analysis and Applications;2023-11