{"paper":{"title":"Sparse reconstruction in spin systems II: Ising and other factor of IID measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.DS","math.MP"],"primary_cat":"math.PR","authors_text":"G\\'abor Pete, P\\'al Galicza","submitted_at":"2024-06-13T15:33:52Z","abstract_excerpt":"For a sequence of Boolean functions $f_n : \\{-1, 1\\}^{V_n} \\longrightarrow \\{-1, 1\\}$, with random input given by some probability measure $\\mathbb{P}_n$, we say that there is sparse reconstruction for $f_n$ if there is a sequence of subsets $U_n \\subseteq V_n$ of coordinates satisfying $|U_n| = o(|V_n|)$ such that knowing the spins in $U_n$ gives us a non-vanishing amount of information about the value of $f_n$.\n  In the first part of this work, we showed that if the $\\mathbb{P}_n$s are product measures, then no sparse reconstruction is possible for any sequence of transitive functions. In th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.09232","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/2406.09232/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"}