{"paper":{"title":"A uniform estimate for rate functions in large deviations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Luchezar Stoyanov","submitted_at":"2016-10-26T03:34:09Z","abstract_excerpt":"Given H\\\"older continuous functions $f$ and $\\psi$ on a sub-shift of finite type $\\Sigma_A^{+}$ such that $\\psi$ is not cohomologous to a constant, the classical large deviation principle holds (\\cite{OP}, \\cite{Kif}, \\cite{Y}) with a rate function $I_\\psi\\geq 0$ such that $I_\\psi (p) = 0$ iff $p = \\int \\psi \\, d \\mu$, where $\\mu = \\mu_f$ is the equilibrium state of $f$. In this paper we derive a uniform estimate from below for $I_\\psi$ for $p$ outside an interval containing $\\tilde{\\psi} = \\int \\psi \\, d\\mu$, which depends only on the sub-shift, the function $f$, the norm $|\\psi|_\\infty$, the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08160","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"}