{"paper":{"title":"Spectral expansion of LQG heat trace and KPZ scaling","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP"],"primary_cat":"math.PR","authors_text":"Jakob Klein, Nathana\\\"el Berestycki","submitted_at":"2026-06-25T12:32:40Z","abstract_excerpt":"Let $h$ be a whole plane Gaussian free field, and let $\\Omega$ be a bounded domain in two dimensions. We study the asymptotics as $t\\to 0$ of the Liouville quantum gravity (LQG) heat trace, defined as the integral over $\\Omega$ of the on-diagonal LQG heat kernel. Our main result is to show that the second term in the spectral expansion as $t\\to 0$ of the expected heat trace is governed by a nontrivial exponent, given by the KPZ (Knizhnik--Polyakov--Zamolodchikov) relation. A similar but stronger (almost sure) result applies to the related notion of heat content. Along the way we obtain various"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.26958","kind":"arxiv","version":1},"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/2606.26958/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"}