{"paper":{"title":"Anomalous diffusion for multi-dimensional critical Kinetic Fokker-Planck equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Camille Tardif, Nicolas Fournier","submitted_at":"2018-12-17T14:40:40Z","abstract_excerpt":"We consider a particle moving in $d\\geq 2$ dimensions, its velocity being a reversible diffusion process, with identity diffusion coefficient, of which the invariant measure behaves, roughly, like $(1+|v|)^{-\\beta}$ as $|v|\\to \\infty$, for some constant $\\beta>0$. We prove that for large times, after a suitable rescaling, the position process resembles a Brownian motion if $\\beta\\geq 4+d$, a stable process if $\\beta\\in [d,4+d)$ and an integrated multi-dimensional generalization of a Bessel process if $\\beta\\in (d-2,d)$. The critical cases $\\beta=d$, $\\beta=1+d$ and $\\beta=4+d$ require special "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.06806","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":""},"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"}