{"paper":{"title":"A matrix model for random nilpotent groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.GR","authors_text":"Anschel Schaffer-Cohen, Kelly Delp, Tullia Dymarz","submitted_at":"2016-02-03T20:39:33Z","abstract_excerpt":"We study random torsion-free nilpotent groups generated by a pair of random words of length $\\ell$ in the standard generating set of $U_n(\\mathbb{Z})$. Specifically, we give asymptotic results about the step properties of the group when the lengths of the generating words are functions of $n$. We show that the threshold function for asymptotic abelianness is $\\ell = c \\sqrt{n}$, for which the probability approaches $e^{-2c^2}$, and also that the threshold function for having full-step, the same step as $U_n(\\mathbb{Z})$, is between $c n^2$ and $c n^3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01454","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":""},"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"}