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…
Random coalescing geodesics in first-passage percolation
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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…