{"paper":{"title":"Estimates on the amplitude of the first Dirichlet eigenvector in discrete frameworks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Laurent Miclo (IMT), Persi Diaconis","submitted_at":"2015-05-28T14:59:55Z","abstract_excerpt":"Consider a finite absorbing Markov generator, irreducible on the non-absorbing states. Perron-Frobenius theory ensures the existence of a corresponding positive eigenvector $\\varphi$. The goal of the paper is to give bounds on the amplitude $\\max \\varphi/\\min\\varphi$. Two approaches are proposed: one using a path method and the other one, restricted to the reversible situation, based on spectral estimates. The latter approach is extended to denumerable birth and death processes absorbing at 0 for which infinity is an entrance boundary. The interest of estimating the ratio is the reduction of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07711","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"}