{"paper":{"title":"The dimension of random subsets of self-similar sets generated by branching random walk","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Lauritz Streck, Pieter Allaart","submitted_at":"2025-06-28T17:32:55Z","abstract_excerpt":"Given a self-similar set $\\Lambda$ that is the attractor of an iterated function system (IFS) $\\{f_1,\\dots,f_N\\}$, consider the following method for constructing a random subset of $\\Lambda$: Let $\\mathbf{p}=(p_1,\\dots,p_N)$ be a probability vector, and label all edges of a full $M$-ary tree independently at random with a number from $\\{1,2,\\dots,N\\}$ according to $\\mathbf{p}$, where $M\\geq 2$ is an arbitrary integer. Then each infinite path in the tree starting from the root receives a random label sequence which is the coding of a point in $\\Lambda$. We let $F\\subset\\Lambda$ denote the set o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.22959","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.22959/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"}