{"paper":{"title":"Tightness of exponential metrics for log-correlated Gaussian fields in arbitrary dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Ewain Gwynne, Jian Ding, Zijie Zhuang","submitted_at":"2023-10-06T03:51:38Z","abstract_excerpt":"We prove the tightness of a natural approximation scheme for an analog of the Liouville quantum gravity metric on $\\mathbb R^d$ for arbitrary $d\\geq 2$. More precisely, let $\\{h_n\\}_{n\\geq 1}$ be a suitable sequence of Gaussian random functions which approximates a log-correlated Gaussian field on $\\mathbb R^d$. Consider the family of random metrics on $\\mathbb R^d$ obtained by weighting the lengths of paths by $e^{\\xi h_n}$, where $\\xi > 0$ is a parameter. We prove that if $\\xi$ belongs to the subcritical phase (which is defined by the condition that the distance exponent $Q(\\xi)$ is greater "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.03996","kind":"arxiv","version":4},"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/2310.03996/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"}