Non-existence of bi-infinite geodesics in the exponential corner growth model

Abstract

This paper gives a self-contained proof of the non-existence of nontrivial bi-infinite geodesics in directed planar last-passage percolation with exponential weights. The techniques used are couplings, coarse graining, and control of geodesics through planarity and estimates derived from increment-stationary versions of the last-passage percolation process.

Keywords

• 60K35
• 60K37
• bi-infinite
• corner growth model
• directed percolation
• geodesic
• random growth model
• last-passage percolation
• queues