Abstract
We consider standard first-passage percolation on $\mathbb{Z}^2$. Geodesics are nearest-neighbor paths in $\mathbb{Z}^2$, each of whose segments is time-minimizing. We prove part of the conjecture that doubly infinite geodesics do not exist. Our main tool is a result of independent interest about the coalescing of semi-infinite geodesics.
Citation
Cristina Licea. Charles M. Newman. "Geodesics in two-dimensional first-passage percolation." Ann. Probab. 24 (1) 399 - 410, January 1996. https://doi.org/10.1214/aop/1042644722
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