{"paper":{"title":"Universality of the cokernels of random $p$-adic matrices with inhomogeneously balanced columns","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.NT","authors_text":"Jungin Lee, Sungjin Park","submitted_at":"2026-06-01T12:37:15Z","abstract_excerpt":"In this paper, we prove universality of the distribution of the cokernels of a random $p$-adic matrix with inhomogeneously balanced columns. More precisely, let $u \\ge 0$ be an integer and $A(n)$ be a random $n \\times (n+u)$ matrix over $\\mathbb{Z}_p$ whose $i$-th column is $\\alpha_n(i)$-balanced. We prove that if $\\sum_{i=1}^{n+u} \\exp(-\\epsilon \\alpha_n(i)n) \\to 0$ as $n \\to \\infty$ for every $\\epsilon>0$, then the cokernels of $A(n)$ converge in distribution, as $n \\to \\infty$, to the same limiting law as the cokernels of Haar-random $n \\times (n+u)$ matrices over $\\mathbb{Z}_p$. This exten"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02180","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/2606.02180/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"}