Stationary cocycles for the corner growth model

Abstract

We study the directed last-passage percolation model on the planar integer lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, outside the class of exactly solvable models. Stationary cocycles are constructed for this percolation model from queueing fixed points. These cocycles serve as boundary conditions for stationary last-passage percolation, define solutions to variational formulas that characterize limit shapes, and yield new results for Busemann functions, geodesics and the competition interface.

69 pages, 10 figures. This submission has been superseded by arXiv:1510.00859 and arXiv:1510.00860 and is no longer updated

References in corpus (1)

• Limiting shape for directed percolation models

Cited by in corpus (3)

• Limit shapes for inhomogeneous corner growth models with exponential and geometric weights
• Stationary cocycles and Busemann functions for the corner growth model
• Variational formulas and cocycle solutions for directed polymer and percolation models