superhomogeneous

English

Etymology

super- +‎ homogeneous

Adjective

superhomogeneous (not comparable)

1. (mathematics) This term needs a definition. Please help out and add a definition, then remove the text {{rfdef}}.
   • 2016, Subhro Ghosh, Joel Lebowitz, “Number rigidity in superhomogeneous random point fields”, in arXiv‎^[1]:

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