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    <id>1741</id>
    <completedYear>2024</completedYear>
    <publishedYear>2024</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber>14 Seiten</pageNumber>
    <edition/>
    <issue>3</issue>
    <volume>34</volume>
    <type>article</type>
    <publisherName>Springer US</publisherName>
    <publisherPlace>New York</publisherPlace>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2024-01-19</completedDate>
    <publishedDate>2024-01-19</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">The minimal spherical dispersion</title>
    <abstract language="eng">We prove upper and lower bounds on the minimal spherical dispersion, improving upon previous estimates obtained by Rote and Tichy in (Anz Österreich Akad Wiss Math Nat Kl 132:3–10, 1995). In particular, we see that the inverse N(ε,d)of the minimal spherical dispersion is, for fixed ε&gt;0, linear in the dimension d of the ambient space. We also derive upper and lower bounds on the expected dispersion for points chosen independently and uniformly at random from the Euclidean unit sphere. In terms of the corresponding inverse N~(ε,d), our bounds are optimal with respect to the dependence on ε.</abstract>
    <parentTitle language="eng">The Journal of Geometric Analysis</parentTitle>
    <identifier type="issn">1050-6926</identifier>
    <identifier type="issn">1559-002X</identifier>
    <identifier type="doi">10.1007/s12220-023-01527-z</identifier>
    <identifier type="urn">urn:nbn:de:101:1-2405020842543.936733306281</identifier>
    <enrichment key="opus.import.date">2025-07-29T13:02:51+00:00</enrichment>
    <enrichment key="opus.source">sword</enrichment>
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    <enrichment key="review.accepted_by">2</enrichment>
    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <author>Joscha Prochno</author>
    <author>Daniel Rudolf</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Dispersion</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Expected dispersion</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Spherical cap</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Spherical dispersion</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>VC-dimension</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="ddc" number="516">Geometrie</collection>
    <collection role="open_access" number="">open_access</collection>
    <collection role="institutes" number="">Fakultät für Informatik und Mathematik</collection>
    <collection role="Import" number="import">Import</collection>
    <collection role="Transformationsvertrag" number="">DEAL Springer Nature</collection>
    <thesisPublisher>Universität Passau</thesisPublisher>
    <file>https://opus4.kobv.de/opus4-uni-passau/files/1741/12220_2024_Article_1527.pdf</file>
  </doc>
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