{"paper":{"title":"Weak coupling limit of a Brownian particle in the curl of the 2D GFF","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Huanyu Yang, Zhilin Yang","submitted_at":"2024-05-09T13:55:00Z","abstract_excerpt":"In this article, we study the weak coupling limit of the following equation in $\\mathbb{R}^2$: $$dX_t^\\varepsilon=\\frac{\\hat{\\lambda}}{\\sqrt{\\log\\frac1\\varepsilon}}\\omega^\\varepsilon(X_t^\\varepsilon)dt+\\nu dB_t,\\quad X_0^\\varepsilon=0. $$ Here $\\omega^\\varepsilon=\\nabla^{\\perp}\\rho_\\varepsilon*\\xi$ with $\\xi$ representing the $2d$ Gaussian Free Field (GFF) and $\\rho_\\varepsilon$ denoting an appropriate identity. $B_t$ denotes a two-dimensional standard Brownian motion, and $\\hat{\\lambda},\\nu>0$ are two given constants. We use the approach from \\cite{Cannizzaro.2023} to show that the second mom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.05778","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/2405.05778/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"}