1 Ocak 2023 Dergi makalesi Açık Erişim

Bayraktar, Turgay; Bloom, Thomas; Levenberg, Norm

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  <dc:creator>Bayraktar, Turgay</dc:creator>
  <dc:creator>Bloom, Thomas</dc:creator>
  <dc:creator>Levenberg, Norm</dc:creator>
  <dc:date>2023-01-01</dc:date>
  <dc:description>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.</dc:description>
  <dc:identifier>https://aperta.ulakbim.gov.trrecord/270930</dc:identifier>
  <dc:identifier>oai:aperta.ulakbim.gov.tr:270930</dc:identifier>
  <dc:rights>info:eu-repo/semantics/openAccess</dc:rights>
  <dc:rights>http://www.opendefinition.org/licenses/cc-by</dc:rights>
  <dc:source>JOURNAL D ANALYSE MATHEMATIQUE 27</dc:source>
  <dc:title>RANDOM POLYNOMIALS IN SEVERAL COMPLEX VARIABLES</dc:title>
  <dc:type>info:eu-repo/semantics/article</dc:type>
  <dc:type>publication-article</dc:type>
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