{"paper":{"title":"Log-correlated Gaussian fields: an overview","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bertrand Duplantier, R\\'emi Rhodes, Scott Sheffield, Vincent Vargas","submitted_at":"2014-07-21T19:21:30Z","abstract_excerpt":"We survey the properties of the log-correlated Gaussian field (LGF), which is a centered Gaussian random distribution (generalized function) $h$ on $\\mathbb R^d$, defined up to a global additive constant. Its law is determined by the covariance formula $$\\mathrm{Cov}\\bigl[ (h, \\phi_1), (h, \\phi_2) \\bigr] = \\int_{\\mathbb R^d \\times \\mathbb R^d} -\\log|y-z| \\phi_1(y) \\phi_2(z)dydz$$ which holds for mean-zero test functions $\\phi_1, \\phi_2$. The LGF belongs to the larger family of fractional Gaussian fields obtained by applying fractional powers of the Laplacian to a white noise $W$ on $\\mathbb R^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5605","kind":"arxiv","version":1},"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"}