{"paper":{"title":"Tropical Limits of Probability Spaces, Part I: The Intrinsic Kolmogorov-Sinai Distance and the Asymptotic Equipartition Property for Configurations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","math.PR"],"primary_cat":"math.MG","authors_text":"Jacobus W. Portegies, Rostislav Matveev","submitted_at":"2017-04-02T13:56:36Z","abstract_excerpt":"The entropy of a finite probability space $X$ measures the observable cardinality of large independent products $X^{\\otimes n}$ of the probability space. If two probability spaces $X$ and $Y$ have the same entropy, there is an almost measure-preserving bijection between large parts of $X^{\\otimes n}$ and $Y^{\\otimes n}$. In this way, $X$ and $Y$ are asymptotically equivalent.\n  It turns out to be challenging to generalize this notion of asymptotic equivalence to configurations of probability spaces, which are collections of probability spaces with measure-preserving maps between some of them.\n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.00297","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"}