{"paper":{"title":"Mean-field limits for non-linear Hawkes processes with inhibition on a Erd\\H{o}s-R\\'{e}nyi-graph","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jakob Stiefel","submitted_at":"2022-07-06T13:22:26Z","abstract_excerpt":"We study a multivariate, non-linear Hawkes process $Z^N$ on a $q$-Erd\\H{o}s-R\\'{e}nyi-graph with $N$ nodes. Each vertex is either excitatory (probability $p$) or inhibitory (probability $1-p$). If $p\\neq\\tfrac12$, we take the mean-field limit of $Z^N$, leading to a multivariate point process $\\bar Z$. We rescale the interaction intensity by $N$ and find that the limit intensity process solves a deterministic convolution equation and all components of $\\bar Z$ are independent. The fluctuations around the mean field limit converge to the solution of a stochastic convolution equation. In the crit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.02655","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/2207.02655/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"}