The Sobol’ sequence is not quasi-uniform in dimension 2

IF 0.8 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society Pub Date : 2024-02-29 DOI:10.1090/proc/16816

Takashi Goda

引用次数: 0

Abstract

Are common quasi-Monte Carlo sequences quasi-uniform? While this question remains widely open, in this short note, we prove that the two-dimensional Sobol’ sequence is not quasi-uniform. This result partially answers an unsolved problem of Sobol’ and Shukhman [Math. Comput. Simulation 75 (2007), pp. 80–86] in a negative manner.

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索布尔序列在维 2 中不是准均匀的

常见的准蒙特卡罗序列是准均匀的吗？尽管这个问题仍然悬而未决，但在这篇短文中，我们证明了二维索博尔序列不是准均匀序列。这一结果以否定的方式部分回答了 Sobol' 和 Shukhman [Math. Comput. Simulation 75 (2007), pp.

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来源期刊

Proceedings of the American Mathematical Society 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

207

审稿时长

2-4 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to shorter research articles (not to exceed 15 printed pages) in all areas of pure and applied mathematics. To be published in the Proceedings, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Longer papers may be submitted to the Transactions of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.