{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/estimating-the-hyperuniformity-exponent-of","title":"Estimating the hyperuniformity exponent of point processes","arxiv_id":"2407.16797","date":"2024-07-23","proceeding":null,"authors":["Gabriel Mastrilli","Bartłomiej Błaszczyszyn","Frédéric Lavancier"],"abstract":"We address the challenge of estimating the hyperuniformity exponent $\\alpha$ 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 $\\log S$. Our estimator is built upon the (expanding window) asymptotic variance of some wavelet transforms of the point process. By combining several scales and several wavelets, we develop a multi-scale, multi-taper estimator $\\widehat{\\alpha}$. We analyze its asymptotic behavior, proving its consistency under various settings, and enabling the construction of asymptotic confidence intervals for $\\alpha$ when $\\alpha < d$ 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 $\\widehat{\\alpha}$. Finally, we investigate the performance of $\\widehat{\\alpha}$ through simulations, and we apply our method to the analysis of hyperuniformity in a real dataset of marine algae.","url_abs":"https://arxiv.org/abs/2407.16797v1","url_pdf":"https://arxiv.org/pdf/2407.16797v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"estimating-the-hyperuniformity-exponent-of","repo_url":"https://github.com/gabrielmastrilli/Estim_Hyperuniformity","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}