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  <doc>
    <id>1887</id>
    <completedYear>2024</completedYear>
    <publishedYear>2024</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber>32 Seiten</pageNumber>
    <edition/>
    <issue>288, 1</issue>
    <volume>2025</volume>
    <type>article</type>
    <publisherName>Elsevier</publisherName>
    <publisherPlace>Amsterdam</publisherPlace>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2024-09-14</completedDate>
    <publishedDate>2024-09-19</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A probabilistic approach to Lorentz balls l(^n)(q,1)</title>
    <abstract language="eng">We develop a probabilistic approach to study the volumetric and geometric properties of unit balls |B(^n)(q,1) of finite-dimensional Lorentz sequence spaces l(^n)(q,1). More precisely, we show that the empirical distribution of a random vector X^(n) uniformly distributed on its volume normalized unit ball converges weakly to a compactly supported symmetric probability distribution with explicitly given density; as a consequence we obtain a weak Poincaré-Maxwell-Borel principle for any fixed number k in |N of coordinates of X^(n) as n grows infinitly. Moreover, we prove a central limit theorem for the largest coordinate of X^(n), demonstrating a quite different behavior than in the case of the l(^n)(q) balls, where a Gumbel distribution appears in the limit. Finally, we prove a Schechtman-Schmuckenschläger type result for the asymptotic volume of intersections of volume normalized l(^n)(q,1) and l(^n)(p) balls.</abstract>
    <parentTitle language="eng">Journal of Functional Analysis (Online ISSN: 1096-0783)</parentTitle>
    <identifier type="doi">10.1016/j.jfa.2024.110682</identifier>
    <identifier type="urn">urn:nbn:de:bvb:739-opus4-18878</identifier>
    <enrichment key="opus.doi.autoCreate">false</enrichment>
    <enrichment key="opus.urn.autoCreate">true</enrichment>
    <enrichment key="review.accepted_by">2</enrichment>
    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <author>Zakhar Kabluchko</author>
    <author>Joscha Prochno</author>
    <author>Mathias Sonnleitner</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Central limit theorem</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Concentration of measure</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Convex body</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Maximum entropy principle</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="open_access" number="">open_access</collection>
    <collection role="institutes" number="">Fakultät für Informatik und Mathematik</collection>
    <collection role="Transformationsvertrag" number="">DEAL Elsevier</collection>
    <thesisPublisher>Universität Passau</thesisPublisher>
    <file>https://opus4.kobv.de/opus4-uni-passau/files/1887/kabluchko_prochno_sonnleitner_lorentz_balls.pdf</file>
  </doc>
</export-example>
