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    <completedYear>2024</completedYear>
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    <pageFirst>422</pageFirst>
    <pageLast>437</pageLast>
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    <volume>259</volume>
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    <title language="eng">The pair correlation function of multi-dimensional low-discrepancy sequences with small stochastic error terms</title>
    <abstract language="deu">In any dimension d≥2, there is no known example of a low-discrepancy sequence which possesses Poisssonian pair correlations. This is in some sense rather surprising, because low-discrepancy sequences always have β-Poissonian pair correlations for all 0&lt;β&lt;1/d and are therefore arbitrarily close to having Poissonian pair correlations (which corresponds to the case β=1/d). In this paper, we further elaborate on the closeness of the two notions. We show that d-dimensional Kronecker sequences for badly approximable vectors α→ with an arbitrary small uniformly distributed stochastic error term generically have β=1/d-Poissonian pair correlations.</abstract>
    <parentTitle language="eng">Journal of Number Theory</parentTitle>
    <identifier type="doi">10.1016/j.jnt.2023.12.011</identifier>
    <enrichment key="opus.import.data">@articleschmiedt_pair_2024, title = The pair correlation function of multi-dimensional low-discrepancy sequences with small stochastic error terms, volume = 259, issn = 0022-314X, url = https://www.sciencedirect.com/science/article/pii/S0022314X24000295, doi = 10.1016/j.jnt.2023.12.011, abstract = In any dimension d≥2, there is no known example of a low-discrepancy sequence which possesses Poisssonian pair correlations. This is in some sense rather surprising, because low-discrepancy sequences always have β-Poissonian pair correlations for all 0&lt;β&lt;1d and are therefore arbitrarily close to having Poissonian pair correlations (which corresponds to the case β=1d). In this paper, we further elaborate on the closeness of the two notions. We show that d-dimensional Kronecker sequences for badly approximable vectors α→ with an arbitrary small uniformly distributed stochastic error term generically have β=1d-Poissonian pair correlations., urldate = 2024-04-22, journal = Journal of Number Theory, author = Schmiedt, Anja and Weiß, Christian, month = jun, year = 2024, keywords = Kronecker sequences, Poissonian pair correlations, Uniform distribution, pages = 422–437, file = ScienceDirect Snapshot:CUsersjach208ZoterostorageQEX9KK2HS0022314X24000295.html:text/html,</enrichment>
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    <author>Anja Bettina Schmiedt</author>
    <author>Christian Weiß</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Kronecker sequences</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Poissonian pair correlations</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Uniform distribution</value>
    </subject>
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