{"paper":{"title":"The blockage problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"A. Troiani, E. R. Speer, J. L. Lebowitz, O. Costin","submitted_at":"2012-07-27T14:38:29Z","abstract_excerpt":"We investigate the totally asymmetric exclusion process on Z, with the jump rate at site i given by r_i=1 for i nonzero, r_0=r. It is easy to see that the maximal stationary current j(r) is nondecreasing in r and that j(r)=1/4 for r>=1; it is a long outstanding problem to determine whether or not the critical value r_c of r such that j(r)=1/4 for r>r_c is strictly less than 1. Here we present a heuristic argument, based on the analysis of the first sixteen terms in a formal power series expansion of j(r) obtained from finite volume systems, that r_c=1 and that for r less than 1 and near 1, j(r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6555","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"}