{"paper":{"title":"Hydrodynamic limits for long-range asymmetric interacting particle systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Doron Shahar, Sunder Sethuraman","submitted_at":"2018-02-27T01:27:43Z","abstract_excerpt":"We consider the hydrodynamic scaling behavior of the mass density with respect to a general class of mass conservative interacting particle systems on ${\\mathbb Z}^n$, where the jump rates are asymmetric and long-range of order $\\|x\\|^{-(n+\\alpha)}$ for a particle displacement of order $\\|x\\|$. Two types of evolution equations are identified depending on the strength of the long-range asymmetry. When $0<\\alpha<1$, we find a new integro-partial differential hydrodynamic equation, in an anomalous space-time scale. On the other hand, when $\\alpha\\geq 1$, we derive a Burgers hydrodynamic equation,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.09674","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"}