{"paper":{"title":"Statistical reconstruction of the Gaussian free field and KT transition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Avelio Sep\\'ulveda, Christophe Garban","submitted_at":"2020-02-27T17:49:35Z","abstract_excerpt":"In this paper, we focus on the following question. Assume $\\phi$ is a discrete Gaussian free field (GFF) on $\\Lambda \\subset \\frac 1 n \\mathbb{Z}^2$ and that we are given $e^{iT \\phi}$, or equivalently $\\phi \\pmod{\\frac {2\\pi} T}$. Can we recover the macroscopic observables of $\\phi$ up to $o(1)$ precision? We prove that this statistical reconstruction problem undergoes the following Kosterlitz-Thouless type phase transition:\n  -) If $T<T_{rec}^-$ , one can fully recover $\\phi$ from the knowledge of $\\phi \\pmod{\\frac {2\\pi} T}$. In this regime our proof relies on a new type of Peierls argument"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.12284","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/2002.12284/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"}