Geodesics and the competition interface 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. 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.

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

References in corpus (3)

• Limiting shape for directed percolation models
• The motion of a second class particle for the tasep starting from a decreasing shock profile
• Inviscid Burgers equation with random kick forcing in noncompact setting