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superhomogeneous (not comparable)

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   • 2016, Subhro Ghosh, Joel Lebowitz, “Number rigidity in superhomogeneous random point fields”, in arXiv‎:

     These conditions are : (a) the variance of the number of particles in a bounded domain ${\displaystyle {\mathcal {O}}\subset \mathbb {R} ^{d}}$ grows slower than the volume of ${\displaystyle {\mathcal {O}}}$ (a.k.a. superhomogeneous point processes), when ${\displaystyle {\mathcal {O}}\uparrow \mathbb {R} ^{d}}$ (in a self-similar manner), and (b) the truncated pair correlation function is bounded by ${\displaystyle C_{1}[|x-y|+1]^{-2}}$ in ${\displaystyle d=1}$ and by ${\displaystyle C_{2}[|x-y|+1]^{-(4+\epsilon )}}$ in ${\displaystyle d=2}$.