{"paper":{"title":"Sampling from the Sherrington-Kirkpatrick Gibbs measure via algorithmic stochastic localization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cs.DS"],"primary_cat":"math.PR","authors_text":"Ahmed El Alaoui, Andrea Montanari, Mark Sellke","submitted_at":"2022-03-10T00:15:22Z","abstract_excerpt":"We consider the Sherrington-Kirkpatrick model of spin glasses at high-temperature and no external field, and study the problem of sampling from the Gibbs distribution $\\mu$ in polynomial time. We prove that, for any inverse temperature $\\beta<1/2$, there exists an algorithm with complexity $O(n^2)$ that samples from a distribution $\\mu^{alg}$ which is close in normalized Wasserstein distance to $\\mu$. Namely, there exists a coupling of $\\mu$ and $\\mu^{alg}$ such that if $(x,x^{alg})\\in\\{-1,+1\\}^n\\times \\{-1,+1\\}^n$ is a pair drawn from this coupling, then $n^{-1}\\mathbb E\\{||x-x^{alg}||_2^2\\}="},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.05093","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2203.05093/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}