Herein, we address the expectations of frame potentials of three types of determinantal point processes (DPPs) on the unit sphere ${\mathbb{S}}^d$: (i) spherical ensembles on ${\mathbb{S}}^2$; (ii) harmonic ensembles on ${\mathbb{S}}^d$ and (iii) jittered sampling point processes on ${\mathbb{S}}^d$. The random point configurations generated by such DPPs converge more rapidly towards finite unit norm tight frames (FUNTFs) than the Poisson point processes on the unit sphere.

中文翻译：

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球体上的有限框架，框架势和行列式点过程

在此，我们解决了单位球面上三种类型的行列式点过程（DPP）的框架势的期望${\mathbb{小号}}^d$：（i）球形合奏 ${\mathbb{小号}}^{\mathrm{2个}}$; （ii）谐波合奏${\mathbb{小号}}^d$ （iii）抖动的采样点过程 ${\mathbb{小号}}^d$。与单位球面上的泊松点过程相比，由此类DPP生成的随机点配置朝有限单位规范紧密框架（FUNTF）收敛更快。