{"paper":{"title":"Time averaged Einstein relation and fluctuating diffusivities for the L\\'evy walk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Daniela Froemberg, Eli Barkai","submitted_at":"2012-11-07T13:21:38Z","abstract_excerpt":"The L\\'evy walk model is a stochastic framework of enhanced diffusion with many applications in physics and biology. Here we investigate the time averaged mean squared displacement $\\bar{\\delta^2}$ often used to analyze single particle tracking experiments. The ballistic phase of the motion is non-ergodic and we obtain analytical expressions for the fluctuations of $\\bar{\\delta^2}$. For enhanced sub-ballistic diffusion we observe numerically apparent ergodicity breaking on long time scales. As observed by Akimoto \\textit{Phys. Rev. Lett.} \\textbf{108}, 164101 (2012) deviations of temporal aver"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1539","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"}