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

Abstract

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.

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

References in corpus (5)

• Airy kernel with two sets of parameters in directed percolation and random matrix theory
• Limiting shape for directed percolation models
• Large deviations for some corner growth models with inhomogeneity
• Directed last passage percolation with discontinuous weights
• Stationary cocycles for the corner growth model

Cited by in corpus (2)

• Stationary measures for two dual families of finite and zero temperature models of directed polymers on the square lattice
• Upper tail large deviations in Brownian directed percolation