A metric result for special subsequences of the Halton sequences

TL;DR

This paper studies a specific subsequence of the Halton sequence, defined by a real parameter, and proves that it exhibits low-discrepancy properties in a metric sense, contributing to the understanding of sequence uniformity.

Contribution

It introduces a new metric analysis of a special subsequence of the Halton sequence, establishing almost low-discrepancy results for this class.

Findings

Proves a metric almost low-discrepancy result for the subsequence

Identifies conditions under which the subsequence maintains low discrepancy

Enhances understanding of the distribution properties of Halton subsequences

Abstract

In this paper we investigate the special subsequence of the Halton sequence indexed by $\lfloor\beta n\rfloor$ with $\beta \in \mathbb{R}$ and prove a metric almost low- discrepancy result.