{"paper":{"title":"Exponential ergodicity and Rayleigh-Schroedinger series for infinite dimensional diffusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Alejandro F. Ramirez","submitted_at":"2009-10-21T12:57:32Z","abstract_excerpt":"We consider an infinite dimensional diffusion on $T^{\\mathbb Z^d}$, where $T$ is the circle, defined by an infinitesimal generator of the form $L=\\sum_{i\\in\\mathbb Z^d}\\left(\\frac{a_i(\\eta)}{2}\\partial^2_i +b_i(\\eta)\\partial_i\\right)$, with $\\eta\\in T^{\\mathbb Z^d}$, where the coefficients $a_i,b_i$ are of finite range, bounded with uniformly bounded second order partial derivatives and the ellipticity assumption $\\inf_{i,\\eta}a_i(\\eta)>0$ is satisfied. We prove that whenever $\\nu$ is an invariant Gibbs measure for this diffusion satisfying the logarithmic Sobolev inequality, then the dynamics"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.4076","kind":"arxiv","version":3},"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"}