{"paper":{"title":"Equipped graded graphs, projective limits of simplices, and their boundaries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A.Vershik","submitted_at":"2015-03-15T16:41:19Z","abstract_excerpt":"In this paper, we develop a theory of equipped graded graphs (or Bratteli diagrams) and an alternative theory of projective limits of finite-dimensional simplices. An equipment is an additional structure on the graph, namely, a system of \"cotransition\" probabilities on the set of its paths. The main problem is to describe all probability measures on the path space of a graph with given cotransition probabilities; it goes back to the problem, posed by E.~B.~Dynkin in the 1960s, of describing exit and entrance boundaries for Markov chains. The most important example is the problem of describing "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04447","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"}