{"paper":{"title":"Fractional Gaussian fields: a survey","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Asad Lodhia, Samuel S. Watson, Scott Sheffield, Xin Sun","submitted_at":"2014-07-21T19:04:30Z","abstract_excerpt":"We discuss a family of random fields indexed by a parameter $s\\in \\mathbb{R}$ which we call the fractional Gaussian fields, given by\n  \\[\n  \\mathrm{FGF}_s(\\mathbb{R}^d)=(-\\Delta)^{-s/2} W,\n  \\] where $W$ is a white noise on $\\mathbb{R}^d$ and $(-\\Delta)^{-s/2}$ is the fractional Laplacian. These fields can also be parameterized by their Hurst parameter $H = s-d/2$. In one dimension, examples of $\\mathrm{FGF}_s$ processes include Brownian motion ($s = 1$) and fractional Brownian motion ($1/2 < s < 3/2$). Examples in arbitrary dimension include white noise ($s = 0$), the Gaussian free field ($s "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5598","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"}