Jack Hanson (City College of NY)

Title: On Doubly-Infinite Geodesics In First-Passage Percolation Above Two Dimensions

Abstract: First-passage percolation (FPP) is the study of the weighted graph metric induced by i.i.d. nonnegative edge weights on $\mathbb{Z}^d$. Many results and conjectures on the model involve the behavior of infinite geodesics: infinite paths whose finite subsegments are geodesics for the FPP metric. In particular, do doubly-infinite geodesics exist? Much progress has been made on this question when $d = 2$, but the methods used there rely heavily on planarity. We will discuss new techniques which rule out a class of bigeodesics when $d > 2$ as well, providing the first results for general dimension. Based on joint works with G. Brito and M. Damron.