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Last passage percolation in macroscopically inhomogeneous media. (English) Zbl 1189.60184
Summary: In this note we investigate the last passage percolation model in the presence of macroscopic inhomogeneity. We analyze how this affects the scaling limit of the passage time, leading to a variational problem that provides an ODE for the deterministic limiting shape of the maximal path. We obtain a sufficient analytical condition for uniquenes of the solution for the variational problem. Consequences for the totally asymmetric simple exclusion process are discussed.

60K35 Interacting random processes; statistical mechanics type models; percolation theory
82D60 Statistical mechanics of polymers
60F10 Large deviations
82B43 Percolation
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