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.

32 pages, 9 figures

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• The stationary horizon and semi-infinite geodesics in the directed landscape
• Global structure of semi-infinite geodesics and competition interfaces in Brownian last-passage percolation
• Optimal-order exit point bounds in exponential last-passage percolation via the coupling technique
• Moderate deviation and exit time estimates for stationary Last Passage Percolation
• Mixing times and cutoff for the TASEP in the high and low density phase
• Intertwining the Busemann process of the directed polymer model
• Geodesic trees in last passage percolation and some related problems