New bounds on the minimal dispersion
New bounds on the minimal dispersion
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DOI：
10.1016/j.jco.2022.101648
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发表时间：
2022-06-10
影响因子：
1.7
通讯作者：
Livshyts, G. V.
中科院分区：
文献类型：
--
作者：
Litvak, A. E.;Livshyts, G. V.
给出了一组近似于[0，1]d中固定体积的轴平行盒的盒的新构造。这改进了单位立方中点集的最小离散度的上界及其在某些区域的周期和非周期设置下的逆离散度。在随机选择点的情况下，我们的界是尖锐的，最高可达双对数倍。我们还将我们的构造应用于k-色散。(C)2022 Elsevier Inc.保留所有权利。
We provide a new construction for a set of boxes approximating axis-parallel boxes of fixed volume in [0, 1]d. This improves upper bounds for the minimal dispersion of a point set in the unit cube and its inverse in both the periodic and non-periodic settings in certain regimes. In the case of random choice of points our bounds are sharp up to double logarithmic factor. We also apply our construction to k-dispersion. (c) 2022 Elsevier Inc. All rights reserved.