{"paper":{"title":"Nonconventional Random Matrix Products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Sasha Sodin, Yuri Kifer","submitted_at":"2018-03-25T09:34:34Z","abstract_excerpt":"Let $\\xi_1,\\xi_2,...$ be independent identically distributed random variables and $F:\\bbR^\\ell\\to SL_d(\\bbR)$ be a Borel measurable matrix-valued function. Set $X_n=F(\\xi_{q_1(n)},\\xi_{q_2(n)},...,\\xi_{q_\\ell(n)})$ where $0\\leq q_1<q_2<...<q_\\ell$ are increasing functions taking on integer values on integers. We study the asymptotic behavior as $N\\to\\infty$ of the singular values of the random matrix product $\\Pi_N=X_N\\cdots X_2X_1$ and show, in particular, that (under certain conditions) $\\frac 1N\\log\\|\\Pi_N\\|$ converges with probability one as $N\\to\\infty$. We also obtain similar results for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09221","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":""},"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"}