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(Non)-hyperuniformity of perturbed lattices

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arxiv 2405.19881 v3 pith:C5DDGAA7 submitted 2024-05-30 math.PR

classification math.PR
keywords hyperuniformperturbationswhenarbitrarilycaseconditionconstructdecay
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abstract

We ask whether a stationary lattice in dimension $d$ whose points are shifted by identically distributed but possibly dependent perturbations remains hyperuniform. When $d = 1$ or $2$, we show that it is the case when the perturbations have a finite $d$-moment, and that this condition is sharp. When $d \geq 3$, we construct arbitrarily small perturbations such that the resulting point process is not hyperuniform. As a side remark of independent interest, we exhibit hyperuniform processes with arbitrarily slow decay of their number variance.

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Cited by 6 Pith papers

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