{"paper":{"title":"A support property for infinite dimensional interacting diffusion processes","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Byron Schmuland, Michael R\\\"ockner","submitted_at":"1998-01-09T00:00:00Z","abstract_excerpt":"The Dirichlet form associated with the intrinsic gradient on Poisson space is known to be quasi-regular on the complete metric space $\\ddot\\Gamma=$ $\\{Z_+$-valued Radon measures on $\\IR^d\\}$. We show that under mild conditions, the set $\\ddot\\Gamma\\setminus\\Gamma$ is $\\e$-exceptional, where $\\Gamma$ is the space of locally finite configurations in $\\IR^d$, that is, measures $\\gamma\\in\\ddot\\Gamma$ satisfying $\\sup_{x\\in\\IR^d}\\gamma(\\{x\\})\\leq 1$. Thus, the associated diffusion lives on the smaller space $\\Gamma$. This result also holds for Gibbs measures with superstable interactions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9801143","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":""},"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"}