{"paper":{"title":"Bounds for distances and geodesic dimension in Liouville first passage percolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Ewain Gwynne, Joshua Pfeffer","submitted_at":"2019-03-22T15:37:28Z","abstract_excerpt":"For $\\xi \\geq 0$, Liouville first passage percolation (LFPP) is the random metric on $\\varepsilon \\mathbb Z^2$ obtained by weighting each vertex by $\\varepsilon e^{\\xi h_\\varepsilon(z)}$, where $h_\\varepsilon(z)$ is the average of the whole-plane Gaussian free field $h$ over the circle $\\partial B_\\varepsilon(z)$. Ding and Gwynne (2018) showed that for $\\gamma \\in (0,2)$, LFPP with parameter $\\xi = \\gamma/d_\\gamma$ is related to $\\gamma$-Liouville quantum gravity (LQG), where $d_\\gamma$ is the $\\gamma$-LQG dimension exponent. For $\\xi > 2/d_2$, LFPP is instead expected to be related to LQG wit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.09561","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":""},"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"}