The affine ensemble: determinantal point processes associated with the 𝑎𝑥 + 𝑏 group

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<p>We introduce the affine ensemble, a class of determinantal point processes (DPP) in the half-plane ℂ+ associated with the 𝑎𝑥 + 𝑏 (affine) group, depending on an admissible Hardy function 𝜓. We obtain the asymptotic behavior of the variance, the exact value of the asymptotic constant, and non-asymptotic upper and lower bounds for the variance on a compact set Ω ⊂ ℂ+. As a special case one recovers the DPP related to the weighted Bergman kernel. When 𝜓 is chosen within a finite family whose Fourier transform are Laguerre functions, we obtain the DPP associated to hyperbolic Landau levels, the eigenspaces of the finite spectrum of the Maass Laplacian with a magnetic field.</p>

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詳細情報 詳細情報について

  • CRID
    1390858784327672960
  • DOI
    10.2969/jmsj/88018801
  • ISSN
    18811167
    18812333
    00255645
  • 本文言語コード
    en
  • データソース種別
    • JaLC
    • Crossref
  • 抄録ライセンスフラグ
    使用不可

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