{"paper":{"title":"Variance of the $SIS$ Epidemic on Networks: A Diffusion Approximation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR","physics.soc-ph","q-bio.QM"],"primary_cat":"cond-mat.stat-mech","authors_text":"Hrvoje \\v{S}tefan\\v{c}i\\'c, Istv\\'an Zolt\\'an Kiss, Lucija Nora Farka\\v{s}, Sebastian Morel Balbi, Vinko Zlati\\'c","submitted_at":"2026-07-03T13:11:26Z","abstract_excerpt":"Functional laws of large numbers (FLLNs) describe the mean-field trajectory of epidemics on networks, but say nothing about the fluctuations around it. These fluctuations are governed by moments of the degree distribution not relevant at the level of the mean. A rigorous functional central limit theorem (FCLT) exists for the susceptible--infected ($SI$) process on configuration-model graphs, but no analogue exists for $SIS$, where recovery reintroduces vertices into the susceptible pool with partially known neighborhoods, breaking the clean neighborhood distribution the $SI$ derivation relies "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.03300","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/2607.03300/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"}