2024/05/30 by David Dereudre, Daniela Flimmel, Dereudre, David +5 · 3 citations
Mathematics · Physics and Astronomy · #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2405.19881
openalex publication_date 2024/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ≥ 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.