The rescaled first-passage percolation metric on the unit box satisfies a large deviation principle at speed n, with a rate function given by an integral against Hausdorff measure of a local cost.
U pper tail large deviations in first passage percolation
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Large deviation principle at speed $n$ for the random metric in first-passage percolation
The rescaled first-passage percolation metric on the unit box satisfies a large deviation principle at speed n, with a rate function given by an integral against Hausdorff measure of a local cost.