{"paper":{"title":"Invariant measures of discrete interacting particle systems: Algebraic aspects","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jean-Fran\\c{c}ois Marckert, Luis Fredes","submitted_at":"2017-11-21T11:03:39Z","abstract_excerpt":"Consider a continuous time particle system $\\eta^t=(\\eta^t(k),k\\in \\mathbb{L})$, indexed by a lattice $\\mathbb{L}$ which will be either $\\mathbb{Z}$, $\\mathbb{Z}/n\\mathbb{Z}$, a segment $\\{1,\\cdots, n\\}$, or $\\mathbb{Z}^d$, and taking its values in the set $E_{\\kappa}^{\\mathbb{L}}$ where $E_{\\kappa}=\\{0,\\cdots,\\kappa-1\\}$ for some fixed $\\kappa\\in\\{\\infty, 2,3,\\cdots\\}$. Assume that the Markovian evolution of the particle system (PS) is driven by some translation invariant local dynamics with bounded range, encoded by a jump rate matrix $T$. These are standard settings, satisfied by the TASEP,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.07713","kind":"arxiv","version":3},"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"}