| Abstract: |
| In First Passage Percolation (FPP) one places nonnegative random weights on the edges of a graph and studies the induced random metric space. In this context, bigeodesics are double infinite paths such that each segment is a geodesic. It has been famously conjectured that bigeodesics do not exist almost surely. We provide the first progress on this question in general dimensions by showing that bigeodesics cannot be constructed as limits of point-to-hyperplane geodesics. |
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