{"paper":{"title":"Free-differentiability conditions on the free-energy function implying large deviations","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Henri Comman","submitted_at":"2005-06-02T15:36:05Z","abstract_excerpt":"Let $(\\mu_{\\alpha})$ be a net of Radon sub-probability measures on the real line, and $(t_{\\alpha})$ be a net in $]0,+\\infty[$ converging to 0. Assuming that the generalized log-moment generating function $L(\\lambda)$ exists for all $\\lambda$ in a nonempty open interval $G$, we give conditions on the left or right derivatives of $L_{\\mid G}$, implying vague (and thus narrow when $0\\in G$) large deviations. The rate function (which can be nonconvex) is obtained as an abstract Legendre-Fenchel transform. This allows us to strengthen the G\\\"{a}rtner-Ellis theorem by removing the usual differentia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0506044","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"}