Large Deviations for Some Corner Growth Models with Inhomogeneity
2017, v.23, Issue 2, 267-312
We study an inhomogeneous generalization of the classical corner growth in which the weights are exponentially distributed with random parameters. Our interest is in the large deviation properties of the last passage times. We obtain tractable variational representations of the right tail large deviation rate functions in both the quenched and annealed settings and estimates for left tail large deviations. We also compute expansions of the right tail rate functions near the shape function, which are consistent with the expectation of KPZ type fluctuations in an appropriate regime.
Keywords: corner growth model; directed last-passage percolation; TASEP; exactly solvable models; large deviations; rate functions