{"paper":{"title":"Spectral gap properties for linear random walks and Pareto's asymptotics for affine stochastic recursions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Emile Le Page (LMAM), Yves Guivarc'H (IRMAR)","submitted_at":"2012-04-26T19:00:39Z","abstract_excerpt":"Let $V=\\mathbb R^d$ be the Euclidean $d$-dimensional space, $\\mu$ (resp $\\lambda$) a probability measure on the linear (resp affine) group $G=G L (V)$ (resp $H= \\Aff (V))$ and assume that $\\mu$ is the projection of $\\lambda$ on $G$. We study asymptotic properties of the iterated convolutions $\\mu^n *\\delta\\_{v}$ (resp $\\lambda^n*\\delta\\_{v})$ if $v\\in V$, i.e asymptotics of the random walk on $V$ defined by $\\mu$ (resp $\\lambda$), if the subsemigroup $T\\subset G$ (resp.\\ $\\Sigma \\subset H$) generated by the support of $\\mu$ (resp $\\lambda$) is \"large\". We show spectral gap properties for the c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.6004","kind":"arxiv","version":5},"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"}