{"paper":{"title":"Markov properties of Gaussian random fields on compact metric graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Alexandre B. Simas, David Bolin, Jonas Wallin","submitted_at":"2023-04-06T16:14:07Z","abstract_excerpt":"There has recently been much interest in Gaussian fields on linear networks and, more generally, on compact metric graphs. One proposed strategy for defining such fields on a metric graph $\\Gamma$ is through a covariance function that is isotropic in a metric on the graph. Another is through a fractional-order differential equation $L^{\\alpha/2} (\\tau u) = \\mathcal{W}$ on $\\Gamma$, where $L = \\kappa^2 - \\nabla(a\\nabla)$ for (sufficiently nice) functions $\\kappa, a$, and $\\mathcal{W}$ is Gaussian white noise. We study Markov properties of these two types of fields. First, we show that no Gaussi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.03190","kind":"arxiv","version":3},"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/2304.03190/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"}