{"paper":{"title":"Some Limit Theorems Regarding Products of Random Matrices I: Directional Derivative of the Lyapunov Exponent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.PR","authors_text":"Fan Wang","submitted_at":"2022-09-16T07:08:54Z","abstract_excerpt":"Given an i.i.d. sequence $\\{A_n(\\omega)\\}_{n\\ge 1}$ of invertible matrices and a random matrix $B(\\omega)$, we consider the random matrix sequences inductively defined by $S_n(\\omega) = A_n(\\omega)S_{n-1}(\\omega)$ and $T_n(\\omega) = B(\\sigma^{n-1}\\omega)S_{n-1}(\\omega)+A_n(\\omega)T_{n-1}(\\omega)$, and study several limit theorems involving $T_n(\\omega)$ as well as the asymptotic behaviour of the action of $T_n(\\omega)$ on the projective space and on the unit circle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.07750","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/2209.07750/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"}