{"paper":{"title":"Heat kernel estimates for nonlocal kinetic operators","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Haojie Hou, Xicheng Zhang","submitted_at":"2024-10-24T10:11:53Z","abstract_excerpt":"In this paper, we employ probabilistic techniques to derive sharp, explicit two-sided estimates for the heat kernel of the nonlocal kinetic operator $$ \\Delta^{\\alpha/2}_v + v \\cdot \\nabla_x, \\quad \\alpha \\in (0, 2),\\ (x,v)\\in {\\mathbb R}^{d}\\times{\\mathbb R}^d,$$ where $ \\Delta^{\\alpha/2}_v $ represents the fractional Laplacian acting on the velocity variable $v$. Additionally, we establish logarithmic gradient estimates with respect to both the spatial variable $x$ and the velocity variable $v$. In fact, the estimates are developed for more general non-symmetric stable-like operators, demons"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.18614","kind":"arxiv","version":2},"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/2410.18614/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"}