{"paper":{"title":"Weighted topological entropy and intersecting random translates of Bedford--McMullen carpets","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Masaki Tsukamoto, Nima Alibabaei","submitted_at":"2026-06-04T11:01:43Z","abstract_excerpt":"We establish a relativised variational principle for the Feng--Huang weighted topological entropy associated with a factor map between dynamical systems. Combined with a recent theorem of Yin, this yields an almost-everywhere equivalence between the Feng--Huang entropy and its combinatorial version on fibers. As an application, we compute the Hausdorff dimension of the intersection of random translates of two Bedford--McMullen carpets. The resulting formula extends the Kenyon--Peres formula from the self-similar to the self-affine setting, and also points to a new problem concerning random mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06012","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.06012/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}