{"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/theoretical-wavelet-ell-1-norm-from-one-point","title":"Theoretical wavelet $\\ell_1$-norm from one-point PDF prediction","arxiv_id":"2406.10033","date":"2024-06-14","proceeding":null,"authors":["Vilasini Tinnaneri Sreekanth","Sandrine Codis","Alexandre Barthelemy","Jean-Luc Starck"],"abstract":"Weak gravitational lensing, resulting from the bending of light due to the presence of matter along the line of sight, is a potent tool for exploring large-scale structures, particularly in quantifying non-Gaussianities. It stands as a pivotal objective for upcoming surveys. In the realm of current and forthcoming full-sky weak-lensing surveys, the convergence maps, representing a line-of-sight integration of the matter density field up to the source redshift, facilitate field-level inference, providing an advantageous avenue for cosmological exploration. Traditional two-point statistics fall short of capturing non-Gaussianities, necessitating the use of higher-order statistics to extract this crucial information. Among the various higher-order statistics available, the wavelet $\\ell_1$-norm has proven its efficiency in inferring cosmology (Ajani et al.2021). However, the lack of a robust theoretical framework mandates reliance on simulations, demanding substantial resources and time. Our novel approach introduces a theoretical prediction of the wavelet $\\ell_1$-norm for weak lensing convergence maps, grounded in the principles of Large-Deviation theory. We present, for the first time, a theoretical prediction of the wavelet $\\ell_1$-norm for convergence maps, derived from the theoretical prediction of their one-point probability distribution. Additionally, we explore the cosmological dependence of this prediction and validate the results on simulations. A comparison of our predicted wavelet $\\ell_1$-norm with simulations demonstrates a high level of accuracy in the weakly non-linear regime. Moreover, we show its ability to capture cosmological dependence, paving the way for a more robust and efficient parameter inference process.","url_abs":"https://arxiv.org/abs/2406.10033v1","url_pdf":"https://arxiv.org/pdf/2406.10033v1.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":"theoretical-wavelet-ell-1-norm-from-one-point","repo_url":"https://github.com/vilasinits/LDT_2cell_l1_norm","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}