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<p>We consider the Ghosh–Peres number rigidity of translation-invariant determinantal point processes on the real line ℝ, whose correlation kernels are induced by the Fourier transform of the indicators of generalized Cantor sets in the unit interval. Our main results show that for any given <i>θ</i> ∈ (0, 1), there exists a generalized Cantor set with Lebesgue measure <i>θ</i>, such that the corresponding determinantal point process is Ghosh–Peres number rigid.</p>

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Number Rigid Determinantal Point Processes Induced by Generalized Cantor Sets

  • 期刊论文

  • 发表日期：

    2026年3月17日

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  • Zhaofeng Lin,
  • Yanqi Qiu,
  • Kai Wang

摘要

We consider the Ghosh–Peres number rigidity of translation-invariant determinantal point processes on the real line ℝ, whose correlation kernels are induced by the Fourier transform of the indicators of generalized Cantor sets in the unit interval. Our main results show that for any given θ ∈ (0, 1), there exists a generalized Cantor set with Lebesgue measure θ, such that the corresponding determinantal point process is Ghosh–Peres number rigid.