{"paper":{"title":"The distribution of the cokernel of a polynomial evaluated at a random integral matrix","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.PR"],"primary_cat":"math.NT","authors_text":"GilYoung Cheong, Myungjun Yu","submitted_at":"2023-03-16T07:40:59Z","abstract_excerpt":"Given a prime $p$, let $P(t)$ be a non-constant monic polynomial in $t$ over the ring $\\mathbb{Z}_{p}$ of $p$-adic integers. Let $X_{n}$ be an $n \\times n$ random matrix over $\\mathbb{Z}_{p}$ with independent entries that lie in any residue class modulo $p$ with probability at most $1 - \\epsilon$ for a fixed real number $0 < \\epsilon < 1$. We prove that as $n \\rightarrow \\infty$, the distribution of the cokernel $\\mathrm{cok}(P(X_{n}))$ of $P(X_{n})$ converges to the distribution given by a finite product of some explicit measures that resemble Cohen--Lenstra measures. For example, the random "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.09125","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2303.09125/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"}