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Joint Continuity and Selberg--ODE Equivalence for the $\mathrm{Sine}_β$ Pair Correlation Function
We address two questions posed by Qu and Valkó in their study of the pair correlation function of the $\mathrm{Sine}_β$ process. First, we prove that the pair correlation function admits a jointly continuous version in the inverse-temperature and spatial parameters on $(0,\infty)\times\mathbb{R}$, r
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