A new variance transfer principle proves 2D Coulomb gases are 2-hyperuniform and 3D ones are 1-hyperuniform while giving optimal perimeter-like number variance for Girko matrix eigenvalues on microscopic and some mesoscopic scales.
(Non)-hyperuniformity of perturbed lattices
3 Pith papers cite this work. Polarity classification is still indexing.
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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.
fields
math.PR 3years
2026 3verdicts
UNVERDICTED 3representative citing papers
Introduces p-uniformity for fluctuation scaling and proves its preservation under transport, enabling new isotropic p-uniform point processes with high p that simulate in linear time.
Variance of second-order statistics for both hyperuniform determinantal and non-hyperuniform Gibbs point processes grows proportionally to ball volume, showing generic non-hyperuniformity.
citing papers explorer
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From smooth to discontinuous kernels: a variance transfer principle for hyperuniform processes
A new variance transfer principle proves 2D Coulomb gases are 2-hyperuniform and 3D ones are 1-hyperuniform while giving optimal perimeter-like number variance for Girko matrix eigenvalues on microscopic and some mesoscopic scales.
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Persistence of asymptotic variance under transport: from hyperfluctuation to stealthy hyperuniformity
Introduces p-uniformity for fluctuation scaling and proves its preservation under transport, enabling new isotropic p-uniform point processes with high p that simulate in linear time.
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(Non-)Hyperuniformity of Second Order Statistics of Point Processes
Variance of second-order statistics for both hyperuniform determinantal and non-hyperuniform Gibbs point processes grows proportionally to ball volume, showing generic non-hyperuniformity.