{"paper":{"title":"Point process convergence of extremes in $K$-symmetric exclusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Adri\\'an Gonz\\'alez Casanova, Michael Conroy, Sunder Sethuraman","submitted_at":"2025-06-14T21:24:20Z","abstract_excerpt":"We consider the behavior of extremal particles in $K$-symmetric exclusion on $\\mathbb{Z}$ when the process starts from certain infinite-particle step configurations where there are no particles to the right of a maximal one. In such a system, the occupancy of a site is limited to at most $K \\geq 1$. Let $X^{(0)}_t\\geq X^{(1)}_t\\geq \\cdots$ denote the order statistics of the particles in the system. We show that the point process $\\sum_{m=0}^\\infty \\delta_{v_t(X_{t/K}^{(m)})}$ converges in distribution as $t \\to \\infty$ to a Poisson random measure on $\\mathbb{R}$ with intensity proportional to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.12632","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.12632/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}