1 Ocak 2023 Dergi makalesi Açık Erişim

Bayraktar, Turgay; Bloom, Thomas; Levenberg, Norm

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{
  "DOI": "10.1007/s11854-023-0316-x", 
  "abstract": "<p>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.</p>", 
  "author": [
    {
      "family": "Bayraktar", 
      "given": " Turgay"
    }, 
    {
      "family": "Bloom", 
      "given": " Thomas"
    }, 
    {
      "family": "Levenberg", 
      "given": " Norm"
    }
  ], 
  "container_title": "JOURNAL D ANALYSE MATHEMATIQUE", 
  "id": "270930", 
  "issued": {
    "date-parts": [
      [
        2023, 
        1, 
        1
      ]
    ]
  }, 
  "page": "27", 
  "title": "RANDOM POLYNOMIALS IN SEVERAL COMPLEX VARIABLES", 
  "type": "article-journal"
}