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arXiv · 1306.1766

Estimates of the Discrepancy Function in Exponential Orlicz Spaces

Gagik Amirkhanyan·Dmitriy Bilyk·Michael T Lacey
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Abstract

We prove that in all dimensions n at least 3, for every integer N there exists a distribution of points of cardinality $ N$, for which the associated discrepancy function D_N satisfies the estimate an estimate, of sharp growth rate in N, in the exponential Orlicz class exp)L^{2/(n+1)}. This has recently been proved by M.~Skriganov, using random digit shifts of binary digital nets, building upon the remarkable examples of W.L.~Chen and M.~Skriganov. Our approach, developed independently, complements that of Skriganov.

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Gagik Amirkhanyan, Dmitriy Bilyk, Michael T Lacey. 2013-06-07. Estimates of the Discrepancy Function in Exponential Orlicz Spaces. https://arxiv.org/abs/1306.1766

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