{"paper":{"title":"Hydrodynamic limits for TASEP with space-time discontinuities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A height-dependent TASEP with space-time discontinuous jump rates has a hydrodynamic limit given by a Lax-Oleinik variational formula for the current.","cross_cats":[],"primary_cat":"math.PR","authors_text":"Enrico Scalas, Jacob Butt, Nicos Georgiou","submitted_at":"2026-05-13T13:31:46Z","abstract_excerpt":"We develop a hydrodynamic theory for a height-dependent version of the totally asymmetric simple exclusion process in which the jump rate at a growth site is sampled from a macroscopic two-dimensional speed function evaluated at the spatial coordinate and the current height level. The speed function is allowed to have discontinuities along locally finitely many curves. Through the TASEP height-function representation, the process is coupled to an inhomogeneous directed last-passage percolation model whose exponential rates vary discontinuously in the two macroscopic LPP coordinates. Combining "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Combining the law of large numbers for this last-passage model with an extension of the variational coupling method, we prove a hydrodynamic limit for the height function and for the associated particle density.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The speed function is allowed to have discontinuities along locally finitely many curves; the proof relies on this local finiteness to control the variational coupling and the envelope formulation at jumps.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The height function of TASEP with space-time discontinuous speed function converges to a deterministic limit given by a Lax-Oleinik variational formula that satisfies a discontinuous Hamilton-Jacobi equation.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A height-dependent TASEP with space-time discontinuous jump rates has a hydrodynamic limit given by a Lax-Oleinik variational formula for the current.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"0ad9d71fad14ed420cf21c06aeecfbda0a1e7447edc169213f21628ca31cb03f"},"source":{"id":"2605.13512","kind":"arxiv","version":1},"verdict":{"id":"b734d5f0-697e-44f1-8a50-70787540bbf5","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T18:20:57.503836Z","strongest_claim":"Combining the law of large numbers for this last-passage model with an extension of the variational coupling method, we prove a hydrodynamic limit for the height function and for the associated particle density.","one_line_summary":"The height function of TASEP with space-time discontinuous speed function converges to a deterministic limit given by a Lax-Oleinik variational formula that satisfies a discontinuous Hamilton-Jacobi equation.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The speed function is allowed to have discontinuities along locally finitely many curves; the proof relies on this local finiteness to control the variational coupling and the envelope formulation at jumps.","pith_extraction_headline":"A height-dependent TASEP with space-time discontinuous jump rates has a hydrodynamic limit given by a Lax-Oleinik variational formula for the current."},"references":{"count":69,"sample":[{"doi":"10.1215/kjm/1250283740","year":2003,"title":"Adimurthi and G. D. Veerappa Gowda,Conservation law with discontinuous flux, J. Math. Kyoto Univ.43(2003), no. 1, 27–70. doi:10.1215/kjm/1250283740","work_id":"a8bc6b50-9171-4bf4-88c7-fa5526b71811","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1007/bf01204214","year":1995,"title":"D. Aldous and P. Diaconis. Hammersley’s interacting particle process and longest increasing subsequences.Probability Theory and Related Fields, 103:199–213, 1995. doi:10.1007/BF01204214","work_id":"8d7941c0-ab55-4dee-87f3-632e8a9c64f0","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1214/24-aihp1482","year":2025,"title":"G. Amir, C. Bahadoran, O. Busani, and E. Saada. Invariant measures for multilane exclusion process.Annales de l’Institut Henri Poincar´ e, Probabilit´ es et Statistiques, 61(3):2184–2234, 2025. doi:10","work_id":"bc44115c-04a4-42aa-bdba-c0bc5f41882b","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"G. Amir, C. Bahadoran, O. Busani, and E. Saada. Hydrodynamics and relaxation limit for multilane exclusion process and related hyperbolic systems.arXiv preprint, arXiv:2501.19355, 2025","work_id":"0cfc18b9-a9b5-43cc-a533-f3d483f19ee8","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1007/s00205-010-0389-4","year":2011,"title":"Archive for Rational Mechanics and Analysis , author =","work_id":"56c8fd29-33b6-46da-89fb-8b48556138a3","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":69,"snapshot_sha256":"2513b1febf64225e09f88b179b1121a8ee0b568f1881a1600e82b5f0791613f9","internal_anchors":1},"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"}