{"paper":{"title":"Rank fluctuations of matrix products and a moment method for growing groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.NT"],"primary_cat":"math.PR","authors_text":"Hoi H. Nguyen, Roger Van Peski","submitted_at":"2024-09-04T21:59:12Z","abstract_excerpt":"We consider the cokernel $G_n = \\mathbf{Cok}(A_{k} \\cdots A_2 A_1)$ of a product of independent $n \\times n$ random integer matrices with iid entries from generic nondegenerate distributions, in the regime where both $n$ and $k$ are sent to $\\infty$ simultaneously. In this regime we show that the cokernel statistics converge universally to the reflecting Poisson sea, an interacting particle system constructed in arXiv:2312.11702, at the level of $1$-point marginals. In particular, $\\operatorname{corank}(A_{k} \\cdots A_2 A_1 \\pmod{p}) \\sim \\log_p k$, and its fluctuations are $O(1)$ and converge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.03099","kind":"arxiv","version":2},"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/2409.03099/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"}