Directed last passage percolation with discontinuous weights

Abstract

We prove that a directed last passage percolation model with discontinuous macroscopic (non-random) inhomogeneities has a continuum limit that corresponds to solving a Hamilton-Jacobi equation in the viscosity sense. This Hamilton-Jacobi equation is closely related to the conservation law for the hydrodynamic limit of the totally asymmetric simple exclusion process. We also prove convergence of a numerical scheme for the Hamilton-Jacobi equation and present an algorithm based on dynamic programming for finding the asymptotic shapes of maximal directed paths.

To appear in Journal of Statistical Physics

References in corpus (2)

• Airy kernel with two sets of parameters in directed percolation and random matrix theory
• Limiting shape for directed percolation models

Cited by in corpus (3)

• Defect-induced phase transition in the asymmetric simple exclusion process
• Generalizations of TASEP in discrete and continuous inhomogeneous space
• Limit shapes for inhomogeneous corner growth models with exponential and geometric weights