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…
On the distribution of the length of the longest increasing subsequence of random permutations
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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…