{"paper":{"title":"Limit Theorems for the Sum of Persistence Barcodes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Takashi Owada","submitted_at":"2016-04-14T07:39:05Z","abstract_excerpt":"Topological Data Analysis (TDA) refers to an approach that uses concepts from algebraic topology to study the \"shapes\" of datasets. The main focus of this paper is persistent homology, a ubiquitous tool in TDA. Basing our study on this, we investigate the topological dynamics of extreme sample clouds generated by a heavy tail distribution on $\\mathbb R^d$. In particular, we establish various limit theorems for the sum of bar lengths in the persistence barcode plot, a graphical descriptor of persistent homology. It then turns out that the growth rate of the sum of the bar lengths and the proper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04058","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"}