{"paper":{"title":"The universality classes in the parabolic Anderson model","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Peter Moerters, Remco van der Hofstad, Wolfgang Koenig","submitted_at":"2005-04-06T12:05:49Z","abstract_excerpt":"We discuss the long time behaviour of the parabolic Anderson model, the Cauchy problem for the heat equation with random potential on $\\Z^d$. We consider general i.i.d. potentials and show that exactly \\emph{four} qualitatively different types of intermittent behaviour can occur. These four universality classes depend on the upper tail of the potential distribution: (1) tails at $\\infty$ that are thicker than the double-exponential tails, (2) double-exponential tails at $\\infty$ studied by G\\\"artner and Molchanov, (3) a new class called \\emph{almost bounded potentials}, and (4) potentials boun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0504102","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"}