Large deviations for some corner growth models with inhomogeneity

Abstract

We study an inhomogeneous generalization of the classical corner growth in which the weights are exponentially distributed with random parameters. Our main interest is in the quenched and annealed large deviation properties of the last passage times. We derive variational representations of the rate functions for right tail large deviations. The quenched rate function can be computed explicitly for certain choices of the parameter distributions. We present a mechanism for rate n left tail annealed large deviations. In the quenched model these deviations have rate strictly greater than n. The annealed right tail rate function is connected to the quenched rate function through a variational problem involving relative entropy. We identify the speed at which the rate functions decay to zero near the shape function.