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 Electronic Communications in Probability > Vol. 13 (2008) > Paper 13 open journal systems 


Last Passage Percolation in Macroscopically Inhomogeneous Media

Leonardo T. Rolla, Instituto de Matemática Pura e Aplicada
Augusto Q. Teixeira, Instituto de Matemática Pura e Aplicada


Abstract
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.


Full text: PDF

Pages: 131-139

Published on: March 5, 2008
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Electronic Communications in Probability. ISSN: 1083-589X