{"paper":{"title":"Reconstruction of log-correlated fields from multiplicative chaos measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Sami Vihko","submitted_at":"2024-08-30T11:51:44Z","abstract_excerpt":"We consider log-correlated random fields $X$ and the associated multiplicative chaos measures $\\mu_{\\gamma,X}$. Our results reconstruct the underlying field $X$ from the multiplicative chaos measure $\\nu_{\\gamma,X}$. The new feature of our results is that we allow the dimension $d$ to be arbitrary and cover also the critical case $\\gamma=\\sqrt{2d}$. In the sub-critical regime $\\gamma<\\sqrt{2d}$, we allow the fields to be mildly non-Gaussian, that is, the field has the decomposition $X=G+H$ with a log-correlated Gaussian field $G$ and a H\\\"older-continuos (not necessarily Gaussian) field $H$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.17219","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/2408.17219/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"}