{"paper":{"title":"On fluctuations of cycles in a finite CW complex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.PR"],"primary_cat":"math.AT","authors_text":"John R. Klein, Michael J. Catanzaro, Vladimir Y. Chernyak","submitted_at":"2017-10-22T18:35:29Z","abstract_excerpt":"We use algebraic topology to study the stochastic mo- tion of cellular cycles in a finite CW complex. Inspired by statis- tical mechanics, we introduce a homological observable called the average current. The latter measures the average flux of the prob- ability in the process. In the low temperature, adiabatic limit, we prove that the average current fractionally quantizes, in which the denominators are combinatorial invariants of the CW complex."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.07995","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"}