Geodesic rays and exponents in ergodic planar first passage percolation

We study first passage percolation on the plane for a family of invariant, ergodic measures on \mathbb{Z}^2. We prove that for all of these models the asymptotic shape is the \ell-1 ball and that there are exactly four infinite geodesics starting at the origin a.s. In addition we determine the... Show more