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On some recent developments in uniform distribution and discrepancy theory. (English) Zbl 1459.11160

Bilyk, Dmitriy (ed.) et al., Discrepancy theory. Berlin: De Gruyter. Radon Ser. Comput. Appl. Math. 26, 1-20 (2020).
Summary: We survey some of the recent developments in uniform distribution and discrepancy theory, which include, in particular, the fact that Poissonian pair correlation implies uniform distribution, the progress on Tusnády’s problem, Levin’s lower bounds for the discrepancy of most low-discrepancy sequences, a link between the small ball inequality and digital nets, various heuristic arguments supporting two conflicting conjectures on the growth of the star-discrepancy of \(d\)-dimensional points set, and different versions of the Stolarsky principle for the discrepancy on the sphere. We discuss known results and pose some open problems and conjectures.
For the entire collection see [Zbl 1454.11006].

MSC:

11K38 Irregularities of distribution, discrepancy
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