{"paper":{"title":"When Do Two Distributions Yield the Same Expected Euler Characteristic Curve in the Thermodynamic Limit?","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Niklas Hellmer, Tobias Fleckenstein","submitted_at":"2024-01-09T14:33:52Z","abstract_excerpt":"Let $F$ be a probability distribution on $\\mathbb{R}^d$ which admits a bounded density. We investigate the Euler characteristic of the \\v{C}ech complex on $n$ points sampled from $F$ i.i.d. as $n\\to\\infty$ in the thermodynamic limit regime. As a main result, we identify a condition for two probability distributions to yield the same expected Euler characteristic under this construction. Namely, this happens if and only if their densities admit the same excess mass transform. Building on work of Bobrowski, we establish a connection between the limiting expected Euler characteristic of any such "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.04580","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/2401.04580/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"}