{"paper":{"title":"Quantitative Convergence for Sequential Interacting Diffusions via Incremental Relative Entropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Xianliang Zhao, Zhenfu Wang","submitted_at":"2026-02-02T04:57:39Z","abstract_excerpt":"We study a lower-triangular system of interacting diffusions in which particle \\(i\\) interacts only with its predecessors through the empirical measure \\(\\mu^{i-1}_t\\). This gives a directed, non-exchangeable approximation of the same McKean--Vlasov diffusion as the classical exchangeable particle system. We introduce an incremental path-space relative entropy adapted to the causal structure, $$ R_i(T) = H \\left(P^{1:i}_{[0,T]}\\,\\middle|\\,P^{1:i-1}_{[0,T]}\\otimes \\bar P_{[0,T]}\\right), $$ and prove the sharp estimate \\(R_i(T)\\lesssim (i-1)^{-1}\\). Furthermore, we obtain convergence of the empi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.01641","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/2602.01641/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"}