Open Access
January 1998 Absence of geodesics in first-passage percolation on a half-plane
Jan Wehr, Jung Woo
Ann. Probab. 26(1): 358-367 (January 1998). DOI: 10.1214/aop/1022855423


An H-geodesic is a doubly infinite path which locally minimizes the passage time in the i.i.d. first passage percolation model on a half-plane H. Under the assumption that the bond passage times are continuously distributed with a finite mean, we prove that, with probability 1, H-geodesics do not exist. As a corollary we show that, with probability 1, any geodesic in the analogous model on the whole plane $\mathbf{Z}^2$ has to intersect all straight lines with rational slopes.


Download Citation

Jan Wehr. Jung Woo. "Absence of geodesics in first-passage percolation on a half-plane." Ann. Probab. 26 (1) 358 - 367, January 1998.


Published: January 1998
First available in Project Euclid: 31 May 2002

zbMATH: 0937.60092
MathSciNet: MR1617053
Digital Object Identifier: 10.1214/aop/1022855423

Primary: 60K35 , 82B44 , 82D30

Keywords: ergodicity , First-passage percolation , Infinite geodesics , large deviation bounds , time-minimizing paths

Rights: Copyright © 1998 Institute of Mathematical Statistics

Vol.26 • No. 1 • January 1998
Back to Top