• Corpus ID: 212628747

Absence of backward infinite paths for first-passage percolation in arbitrary dimension

  title={Absence of backward infinite paths for first-passage percolation in arbitrary dimension},
  author={Gerandy Brito and Michael Damron and Jack Hanson},
  journal={arXiv: Probability},
In first-passage percolation (FPP), one places nonnegative random variables (weights) $(t_e)$ on the edges of a graph and studies the induced weighted graph metric. We consider FPP on $\mathbb{Z}^d$ for $d \geq 2$ and analyze the geometric properties of geodesics, which are optimizing paths for the metric. Specifically, we address the question of existence of bigeodesics, which are doubly-infinite paths whose subpaths are geodesics. It is a famous conjecture originating from a question of… 

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