1 Ocak 2023 Dergi makalesi Açık Erişim

Bayraktar, Turgay; Bloom, Thomas; Levenberg, Norm

DataCite XML

<?xml version='1.0' encoding='utf-8'?>
<resource xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://datacite.org/schema/kernel-4" xsi:schemaLocation="http://datacite.org/schema/kernel-4 http://schema.datacite.org/meta/kernel-4.1/metadata.xsd">
  <identifier identifierType="URL">https://aperta.ulakbim.gov.tr/record/270930</identifier>
  <creators>
    <creator>
      <creatorName>Bayraktar, Turgay</creatorName>
      <givenName>Turgay</givenName>
      <familyName>Bayraktar</familyName>
      <affiliation>Sabanci Univ, Fac Engn &amp; Nat Sci, TR-34956 Tuzla, Istanbul, Turkiye</affiliation>
    </creator>
    <creator>
      <creatorName>Bloom, Thomas</creatorName>
      <givenName>Thomas</givenName>
      <familyName>Bloom</familyName>
      <affiliation>Univ Toronto, Dept Math, Toronto, ON M5S 2E4, Canada</affiliation>
    </creator>
    <creator>
      <creatorName>Levenberg, Norm</creatorName>
      <givenName>Norm</givenName>
      <familyName>Levenberg</familyName>
      <affiliation>Indiana Univ, Dept Math, Bloomington, IN 47405 USA</affiliation>
    </creator>
  </creators>
  <titles>
    <title>Random Polynomials In Several Complex Variables</title>
  </titles>
  <publisher>Aperta</publisher>
  <publicationYear>2023</publicationYear>
  <dates>
    <date dateType="Issued">2023-01-01</date>
  </dates>
  <resourceType resourceTypeGeneral="Text">Journal article</resourceType>
  <alternateIdentifiers>
    <alternateIdentifier alternateIdentifierType="url">https://aperta.ulakbim.gov.tr/record/270930</alternateIdentifier>
  </alternateIdentifiers>
  <relatedIdentifiers>
    <relatedIdentifier relatedIdentifierType="DOI" relationType="IsIdenticalTo">10.1007/s11854-023-0316-x</relatedIdentifier>
  </relatedIdentifiers>
  <rightsList>
    <rights rightsURI="http://www.opendefinition.org/licenses/cc-by">Creative Commons Attribution</rights>
    <rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
  </rightsList>
  <descriptions>
    <description descriptionType="Abstract">&lt;p&gt;We generalize some previous results on random polynomials in several complex variables. A standard setting is to consider random polynomials H-n(z) := Sigma(mn)(j=1) a(j)p(j)(z) that are linear combinations of basis polynomials {p(j)} with i.i.d. complex random variable coefficients {a(j)} where {p(j)} form an orthonormal basis for a Bernstein-Markov measure on a compact set K subset of C-d. Here mn is the dimension of P-n, the holomorphic polynomials of degree at most n in C-d. We consider more general bases {p(j)}, which include, e.g., higher-dimensional generalizations of Fekete polynomials. Moreover we allow H-n(z) := Sigma(mn)(j=1) a(nj)p(nj)(z), i.e., we have an array of basis polynomials {p(nj)} and random coefficients {a(nj)}. This always occurs in a weighted situation. We prove results on convergence in probability and on almost sure convergence of 1/n log vertical bar H-n vertical bar in L-loc(1)(C-d) to the (weighted) extremal plurisubharmonic function for K. We aim for weakest possible sufficient conditions on the random coefficients to guarantee convergence.&lt;/p&gt;</description>
  </descriptions>
</resource>