# 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}
}
• 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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50 years of first passage percolation
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We celebrate the 50th anniversary of one the most classical models in probability theory. In this survey, we describe the main results of first passage percolation, paying special attention to the
A Surface View of First-Passage Percolation
Let $$\tilde B$$(t) be the set of sites reached from the origin by time t in standard first-passage percolation on Z d , and let B0 (roughly lim $$\tilde B$$ (t)/t) be its deterministic asymptotic
Geodesics in two-dimensional first-passage percolation
• Mathematics
• 1996
We consider standard first-passage percolation on Z 2 . Geodesics are nearest-neighbor paths in Z 2 , each of whose segments is time-minimizing. We prove part of the conjecture that doubly infinite