{"paper":{"title":"Upper bounds on Liouville first passage percolation and Watabiki's prediction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jian Ding, Subhajit Goswami","submitted_at":"2016-10-31T16:21:35Z","abstract_excerpt":"Given a planar continuum Gaussian free field $h^{\\mathcal U}$ in a domain $\\mathcal U$ with Dirichlet boundary condition and any $\\delta>0$, we let $\\{h_\\delta^{\\mathcal U}(v): v\\in \\mathcal U\\}$ be a real-valued smooth Gaussian process where $h_\\delta^{\\mathcal U}(v)$ is the average of $h^{\\mathcal U}$ along a circle of radius $\\delta$ with center $v$. For $\\gamma > 0$, we study the Liouville first passage percolation (in scale $\\delta$), i.e., the shortest path distance in $\\mathcal U$ where the weight of each path $P$ is given by $\\int_P \\mathrm{e}^{\\gamma h_\\delta^{\\mathcal U}(z)} |dz|$. W"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09998","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/1610.09998/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"}