On variants of the Halton sequence



Jassova, Alena, Lertchoosakul, Poj and Nair, Radhakrishnan
(2016) On variants of the Halton sequence. MONATSHEFTE FUR MATHEMATIK, 180 (4). pp. 743-764.

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Abstract

A generalisation of the classical Halton sequence (ϕβ(n))n∈N has emerged in recent years based on β-adic expansions of elements of [0, 1). In the case where β is a natural number greater than 1, this reduces to the classical Halton sequence. In this paper, we use ergodic and analytic methods to prove the uniform distribution of a sequence (ϕβ(kj))j∈N for the sequence of integers (kj)j≥0, which is both Hartman uniformly distributed and good universal. This builds on earlier work of M. Hofer, M. R. Iaco and R. Tichy in the special case kj=j(j=0,1,…). Variants of this phenomenon are also studied.

Item Type: Article
Uncontrolled Keywords: Hartman uniformly distributed sequences, Halton sequences and beta-transformations
Subjects: ?? Q1 ??
?? QA ??
Depositing User: Symplectic Admin
Date Deposited: 05 Aug 2015 08:32
Last Modified: 16 Dec 2022 16:06
DOI: 10.1007/s00605-015-0794-8
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/2018924