{"paper":{"title":"Cutoff and discrete Product Structure in ASEP","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Peter Nejjar","submitted_at":"2018-12-31T18:22:45Z","abstract_excerpt":"We consider the asymmetric simple exclusion process (ASEP) on $\\mathbb{Z}$ with an initial data such that in the large time particle density $\\rho(\\cdot)$ a discontinuity at the origin is created, where the value of $\\rho$ jumps from zero to one, but $\\rho(-\\varepsilon),1-\\rho(\\varepsilon) >0 $ for any $\\varepsilon>0$. We consider the position of a particle $x_{M}$ macroscopically located at the discontinuity, and show that its limit law has a cutoff under $t^{1/2}$ scaling. Inside the discontinuity region, we show that a discrete product limit law arises, which bounds from above the limiting "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.11939","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"}