Graduate Student Analysis Seminar: Limits and Geodesics in First Passage Percolation Models

Assigning i.i.d. weights to the nearest neighbor edges in \$\mathbb{Z}^d\$ gives rise to one of the most natural random metrics on \$\mathbb{Z}^d\$. Despite the metric being easily constructible, it has some surprising geometric properties due to the complicated dependence relation with shortest paths. In this talk, we will explore some well-known results of this metric in the study of First Passage Percolation such as the convergence of balls and the number of infinite geodesics, as well as the techniques used to prove them.