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In this note we investigate the last passage percolation model in thepresence of macroscopic inhomogeneity. We analyze how this affects the scalinglimit of the passage time, leading to a variational problem that provides anODE for the deterministic limiting shape of the maximal path. We obtain asufficient analytical condition for uniqueness of the solution for thevariational problem. Consequences for the totally asymmetric simple exclusionprocess are discussed.

Last Passage Percolation in Macroscopically Inhomogeneous Media