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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. 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