{"paper":{"title":"Continuous time random walks and the Cauchy problem for the heat equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gast\\'on Beltritti, Hugo Aimar, Ivana G\\'omez","submitted_at":"2015-01-09T13:15:35Z","abstract_excerpt":"In this paper we deal with anomalous diffusions induced by Continuous Time Random Walks - CTRW in $\\mathbb{R}^n$. A particle moves in $\\mathbb{R}^n$ in such a way that the probability density function $u(\\cdot,t)$ of finding it in region $\\Omega$ of $\\mathbb{R}^n$ is given by $\\int_{\\Omega}u(x,t) dx$. The dynamics of the diffusion is provided by a space time probability density $J(x,t)$ compactly supported in $\\{t\\geq 0\\}$. For $t$ large enough, $u$ must satisfy the equation $u(x,t)=[(J-\\delta)\\ast u](x,t)$ where $\\delta$ is the Dirac delta in space time. We give a sense to a Cauchy type probl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02127","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"}