{"paper":{"title":"On Kesten's Multivariate Choquet-Deny Lemma","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Sebastian Mentemeier","submitted_at":"2013-02-21T14:01:22Z","abstract_excerpt":"Let $d >1$ and $(A_n)_{n \\ge 1}$ be a sequence of independent identically distributed random matrices with nonnegative entries and no zero column. This induces a Markov chain $M_n = A_n M_{n-1}$ on the cone of d-vectors with nonnegative entries. We study harmonic functions of this Markov chain. Considering a polar decomposition $M_n = X_n \\exp(S_n)$, where $X_n$ is a vector of unit length, and $S_n$ a real valued random variable, it is in particular shown that all \"compound\" harmonic functions $L(x,s)=f(x)g(s)$ are constant. The idea of the proof is originally due to Kesten [Renewal theory for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5284","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":""},"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"}