Last Passage Percolation in Macroscopically Inhomogeneous Media

Leonardo Rolla, Augusto Teixeira
2008 Electronic Communications in Probability  
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 uniqueness of the solution for the variational problem. Consequences for the totally asymmetric simple exclusion process are discussed.
doi:10.1214/ecp.v13-1287 fatcat:jqbaccl4rzbvzfzhwq5ygofmzu