Year: 2026
Type: article
Abstract: We address the challenge of estimating the hyperuniformity exponent α of a spatial point process, given only one realization of it. Assuming that the structure factor S of the point process follows a vanishing power law at the origin (the typical case of a hyperuniform point process), this exponent is defined as the slope near the origin of logS. Our estimator is built upon the (expanding window) asymptotic variance of some shot-noise wavelet transforms, of the point process. By combining several scales and several wavelets, we develop a multi-scale, multi-taper estimator αˆ. We analyze its asymptotic behavior, proving its consistency under various settings, and enabling the construction of asymptotic confidence intervals for α when α<d and under Brillinger mixing. This construction is derived from a multivariate central limit theorem where the normalisations are non-standard and vary among the components. We also present a non-asymptotic deviation inequality providing insights into the influence of tapers on the bias-variance trade-off of αˆ. Finally, we investigate the performance of αˆ through simulations, and we apply our method to the analysis of hyperuniformity in a real dataset of marine algae.
Source: Bernoulli
DOI: 10.3150/26-bej1989
Institutions: Centre National de la Recherche Scientifique, École Nationale de la Statistique et de l'Analyse de l'Information, Centre de Recherche en Économie et Statistique, Université de Rennes, Institut national de recherche en sciences et technologies du numérique, Université Paris Sciences et Lettres, École Normale Supérieure - PSL, DYOGENE: Dynamics of Geometric Networks
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4400968434