{"paper":{"title":"Mean-field theory via dissociated arrays for particle systems interacting through noisy weights","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Datong Zhou, Nicolas Fournier","submitted_at":"2026-06-10T14:31:31Z","abstract_excerpt":"We study a mean-field limit for a $N$-particle system in which each particle follows a diffusion and interacts with other particles through a weight on each directed edge. Each weight evolves according to its own nonlinear SDE driven by a Brownian motion, with coefficients involving the states of the two endpoint particles of the edge. The initial vertex and edge variables are assumed to have a dissociated Aldous--Hoover form. We construct the limiting nonlinear SDE by averaging the interaction over an independent neighbor and an edge input, prove its well-posedness, and show that the dissocia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.12135","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/2606.12135/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"}