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That is, the probability that the random walk jumps from a site $x$ to a nearest neighboring site $x+e$ is given by $p(e)+\\epsilon \\xi(x,e)$, where $p(e)$ is deterministic, $\\{\\{\\xi(x,e):|e|_1=1\\}:x\\in\\mathbb Z^d\\}$ are i.i.d. and $\\epsilon>0$ is a parameter which is eventually chosen small enough. We establish an asymptotic expansion in $\\epsilon$ for the invariant measure of the environmental process whenever a ballisticity condition is satisfied. 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Ramirez, David Campos","submitted_at":"2015-11-10T00:33:05Z","abstract_excerpt":"We consider a random walk in random environment in the low disorder regime on $\\mathbb Z^d$. That is, the probability that the random walk jumps from a site $x$ to a nearest neighboring site $x+e$ is given by $p(e)+\\epsilon \\xi(x,e)$, where $p(e)$ is deterministic, $\\{\\{\\xi(x,e):|e|_1=1\\}:x\\in\\mathbb Z^d\\}$ are i.i.d. and $\\epsilon>0$ is a parameter which is eventually chosen small enough. We establish an asymptotic expansion in $\\epsilon$ for the invariant measure of the environmental process whenever a ballisticity condition is satisfied. 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