{"paper":{"title":"Contraction in the Wasserstein metric for some Markov chains, and applications to the dynamics of expanding maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Artur Lopes, Benoit Kloeckner (LAMA), Manuel Stadlbauer","submitted_at":"2014-12-02T10:35:32Z","abstract_excerpt":"We employ techniques from optimal transport in order to prove decay of transfer operators associated to iterated functions systems and expanding maps, giving rise to a new proof without requiring a Doeblin-Fortet (or Lasota-Yorke) inequality. Our main result is the following. Suppose $T$ is an expanding transformation acting on a compact metric space $M$ and $A: M \\to \\mathbb{R}$ a given fixed H{\\\"o}lder function, and denote by $L$ the Ruelle operator  associated to $A$. We show that if $L$ is normalized (i.e. if $L(1)=1$), then the dual transfer operator $L^*$ is an exponential contraction on"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0848","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"}