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Dey, Shirshendu Chatterjee","submitted_at":"2013-09-23T10:41:06Z","abstract_excerpt":"We consider a model of long-range first-passage percolation on the $d$ dimensional square lattice $Z^d$ in which any two distinct vertices $x, y \\in Z^d$ are connected by an edge having exponentially distributed passage time with mean $||x-y||^{\\alpha+o(1)}$, where $\\alpha>0$ is a fixed parameter and $||\\cdot||$ is the $\\ell_1$-norm on $Z^d$. We analyze the asymptotic growth rate of the set $B_t$, which consists of all $x \\in Z^d$ such that the first-passage time between the origin 0 and $x$ is at most $t$, as $t\\to\\infty$. 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