Number rigid determinantal point processes induced by generalized Cantor sets

Zhaofeng Lin; Yanqi Qiu; Kai Wang

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arXiv · 2407.14168

Number rigid determinantal point processes induced by generalized Cantor sets

Zhaofeng Lin·Yanqi Qiu·Kai Wang

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Abstract

We consider the Ghosh-Peres number rigidity of translation-invariant determinantal point processes on the real line $\mathbb{R}$, 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 $\theta\in(0,1)$, there exists a generalized Cantor set with Lebesgue measure $\theta$, such that the corresponding determinantal point process is Ghosh-Peres number rigid.

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Zhaofeng Lin, Yanqi Qiu, Kai Wang. 2024-07-19. Number rigid determinantal point processes induced by generalized Cantor sets. https://arxiv.org/abs/2407.14168

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