Geodesics and the competition interface for the corner growth model
Probability
2016-07-26 v2
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. In a previous paper we constructed stationary cocycles and Busemann functions for this model. Using these objects, we prove new results on the competition interface, on existence, uniqueness, and coalescence of directional semi-infinite geodesics, and on nonexistence of doubly infinite geodesics.
Cite
@article{arxiv.1510.00860,
title = {Geodesics and the competition interface for the corner growth model},
author = {Nicos Georgiou and Firas Rassoul-Agha and Timo Seppäläinen},
journal= {arXiv preprint arXiv:1510.00860},
year = {2016}
}
Comments
32 pages, 1 figure. Some additions and corrections. Appendix A on coalescence of cocycle geodesics has been omitted but can be found in version 1 of this submission. To appear in Probability Theory and Related Fields