Elnur, Emrah Limit shapes for inhomogeneous corner growth models with exponential and geometric weights. (English) Zbl 1338.60229 Electron. Commun. Probab. 21, Paper No. 42, 16 p. (2016). Summary: 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 \((a_i)_{i \geq 1}\) and \((b_j)_{j \geq 1}\) 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. Cited in 11 Documents MSC: 60K35 Interacting random processes; statistical mechanics type models; percolation theory 60K37 Processes in random environments Keywords:corner growth model; directed last-passage percolation; exactly solvable models; limit shape × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid