For general i.i.d. weights, the midpoint of the geodesic between (0,0) and (n,n) lying at position n/2+tn has probability e^{-2nJ_t(μ0)+o(n)}.
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Large deviations of geodesic midpoint fluctuations in last-passage percolation with general i.i.d. weights
For general i.i.d. weights, the midpoint of the geodesic between (0,0) and (n,n) lying at position n/2+tn has probability e^{-2nJ_t(μ0)+o(n)}.