Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2016
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/1606.02449 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- Given an infinite connected graph, a way to randomly perturb its metric is to assign random i.i.d. lengths to the edges. An open question attributed to Furstenberg is whether there exists a two-sided infinite geodesic in first passage percolation on Z^2, and more generally on Z^n for n>1. Although the answer is generally conjectured to be negative, we give a positive answer for graphs satisfying some negative curvature assumption. Assuming only strict positivity and finite exponential moment for the random lengths, we prove that if a graph X has bounded degree and contains a Morse geodesic (e.g. is non-elementary Gromov hyperbolic), then almost surely, there exists a bi-infinite geodesic in first passage percolation on X.