Stationary cocycles for the corner growth model
Probability
2015-10-07 v3
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.
Cite
@article{arxiv.1404.7786,
title = {Stationary cocycles for the corner growth model},
author = {Nicos Georgiou and Firas Rassoul-Agha and Timo Seppäläinen},
journal= {arXiv preprint arXiv:1404.7786},
year = {2015}
}
Comments
69 pages, 10 figures. This submission has been superseded by arXiv:1510.00859 and arXiv:1510.00860 and is no longer updated