{"paper":{"title":"Diffusion and Relaxation Controlled by Tempered \\alpha-stable Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.data-an"],"primary_cat":"cond-mat.stat-mech","authors_text":"Aleksander Stanislavsky, Aleksander Weron, Karina Weron","submitted_at":"2011-11-13T14:26:10Z","abstract_excerpt":"We derive general properties of anomalous diffusion and nonexponential relaxation from the theory of tempered \\alpha-stable processes. Its most important application is to overcome the infinite-moment difficulty for the \\alpha-stable random operational time \\tau. The tempering results in the existence of all moments of \\tau. The subordination by the inverse tempered \\alpha-stable process provides diffusion(relaxation) that occupies an intermediate place between subdiffusion (Cole-Cole law) and normal diffusion (exponential law). Here we obtain explicitly the Fokker-Planck equation, the mean sq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3018","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"}