Bigeodesics in First-Passage Percolation

@article{Damron2015BigeodesicsIF,
  title={Bigeodesics in First-Passage Percolation},
  author={Michael Damron and Jack Hanson},
  journal={Communications in Mathematical Physics},
  year={2015},
  volume={349},
  pages={753-776}
}
  • M. Damron, J. Hanson
  • Published 2 December 2015
  • Mathematics
  • Communications in Mathematical Physics
In first-passage percolation, we place i.i.d. continuous weights at the edges of $${\mathbb{Z}^2}$$Z2 and consider the weighted graph metric. A distance-minimizing path between points x and y is called a geodesic, and a bigeodesic is a doubly-infinite path whose segments are geodesics. It is a famous conjecture that almost surely, there are no bigeodesics. In the 1990s, Licea–Newman showed that, under a curvature assumption on the “asymptotic shape,” all infinite geodesics have an asymptotic… 
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