{"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/the-gaussian-entropy-map-in-valued-fields","title":"The Gaussian entropy map in valued fields","arxiv_id":"2101.00767","date":"2021-01-04","proceeding":null,"authors":["Yassine El Maazouz"],"abstract":"We exhibit the analog of the entropy map for multivariate Gaussian distributions on local fields. As in the real case, the image of this map lies in the supermodular cone and it determines the distribution of the valuation vector. In general, this map can be defined for non-archimedian valued fields whose valuation group is an additive subgroup of the real line, and it remains supermodular. We also explicitly compute the image of this map in dimension 3.","url_abs":"https://arxiv.org/abs/2101.00767v6","url_pdf":"https://arxiv.org/pdf/2101.00767v6.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":"the-gaussian-entropy-map-in-valued-fields","repo_url":"https://github.com/yassineELMAAZOUZ/Local_field-Gaussians","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"the-gaussian-entropy-map-in-valued-fields","repo_url":"https://github.com/yassineELMAAZOUZ/Gaussian-entropy-map-in-valued-fields","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}