Limit shapes for inhomogeneous corner growth models with exponential and geometric weights

摘要

We generalize the exactly solvable corner growth models by choosing the rateof the exponential distribution $a_i+b_j$ and the parameter of the geometricdistribution $a_i b_j$ at site $(i, j)$, where $(a_i)_{i \ge 1}$ and $(b_j)_{j\ge 1}$ are jointly ergodic random sequences. We identify the shape function interms of a simple variational problem, which can be solved explicitly in somespecial cases.