Limit shapes for inhomogeneous corner growth models with exponential and geometric weights
Elnur Emrah
备注：
14 pages, 1 figure. Revised and shortened version with added references. This version also fixes a mistake in the proof of Theorem 2.3 (now Theorem 2.2). Electron. Commun. Probab. Electron. Commun. Probab. Volume 21 (2016), paper no. 42, 16 pp
We generalize the exactly solvable corner growth models by choosing the rate of the exponential distribution $a_i+b_j$ and the parameter of the geometric distribution $a_i b_j$ 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 in terms of a simple variational problem, which can be solved explicitly in some special cases.
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