{"paper":{"title":"Monge-Amp\\`ere gravitating fluids. Least action principles and particle systems","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Christian L\\'eonard, Roya Mohayaee","submitted_at":"2025-03-03T13:49:57Z","abstract_excerpt":"The Monge-Amp\\`ere gravitation theory (MAG) was introduced by Brenier in 2011 to obtain an approximate solution of the early Universe reconstruction problem. It is a modification of Newtonian gravitation which is based on quadratic optimal transport. Later, Brenier in 2016, then Ambrosio, Baradat and Brenier in 2020 discovered a double large deviation principle for Brownian particles whose rate function is precisely MAG's action functional.\n  In the present article, following Brenier we first recap MAG's theory. Then, we slightly extend it from particles to fluid. This allows us to revisit the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.01537","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}