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

作者：Emrah Elnur^*

来源：Electronic Communications in Probability, 2016, 21(0): 42.

DOI：10.1214/16-ECP4

• corner growth model
• directed last-passage percolation
• exactly solvable models
• limit shape

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 >= 1) and (b(j))(j >= 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.

• 出版日期2016