{"paper":{"title":"Time-Average Based on Scaling Law in Anomalous Diffusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Hyun-Joo Kim","submitted_at":"2014-09-03T04:48:01Z","abstract_excerpt":"To solve the obscureness in measurement brought about from the weak ergodicity breaking appeared in anomalous diffusions we have suggested the time-averaged mean squared displacement (MSD) $\\bar{\\delta^2 (\\tau)}_\\tau$ with a integral interval depending linearly on the lag time $\\tau$. For the continuous time random walk describing a subdiffusive behavior, we have found that $\\bar{\\delta^2 (\\tau)}_\\tau \\sim \\tau^\\gamma$ like that of the ensemble-averaged MSD, which makes it be possible to measure the proper exponent values through time-average in experiments like a single molecule tracking. Als"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0949","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":""},"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"}