Geodesics in Two Dimensional First-Passage Percolation
A geodesic in first-passage percolation on Zd is a doubly infinite path whose finite segments are time-minimizing. A general conjecture says that there are no geodesics in the plane, i.e., for d=2. (This is related to the existence of a nontrivial ground state in a disordered Ising model.) In this talk, we show that there is no geodesic in a half-plane.