Non-existence of bi-infinite geodesics in the exponential corner growth model. (English) Zbl 1456.60248
Summary: 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.
MSC:
| 60K35 | Interacting random processes; statistical mechanics type models; percolation theory |
| 60K37 | Processes in random environments |
| 82B43 | Percolation |
Keywords:
bi-infinite; corner growth model; directed percolation; geodesic; random growth model; last-passage percolation; queuesReferences:
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