In exponential directed last-passage percolation, the full family of semi-infinite geodesics is characterized: unique coalescing trees in all but a countable dense set of directions, exactly two trees in the exceptional directions, which coincide with Busemann measure support and competition…
Non-existence of bi-infinite geodesics in the exponential corner growth model
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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.
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2019 1verdicts
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Geometry of geodesics through Busemann measures in directed last-passage percolation
In exponential directed last-passage percolation, the full family of semi-infinite geodesics is characterized: unique coalescing trees in all but a countable dense set of directions, exactly two trees in the exceptional directions, which coincide with Busemann measure support and competition…