EVENT DETAILS AND ABSTRACT

Title: Tail bounds for the averaged empirical distribution on a geodesic in first-passage percolation
Speaker: Wai-Kit Lam
Speaker Info: University of Minnesota
Brief Description:
Special Note:
Abstract:

Consider $\mathbb{Z}^d$ with nearest-neighbor edges. In first-passage percolation, we place i.i.d. nonnegative weights $(t_e)$ on the edges, and study the induced graph metric $T(x,y)$. A geodesic is a minimizing path for this metric. In a joint work with M. Damron, C. Janjigian and X. Shen, we study the empirical distribution on a geodesic $\gamma$ from $0$ to $x$: $\nu^x(B) := (\text{number of edges } e \text{ in } \gamma \text{ with } t_e \in B) / (\text{number of edges } e \text{ in } \gamma)$. We establish bounds for the averaged empirical distribution $E \nu^x(B)$, particularly showing that if the law of $t_e$ has finite moments of any order strictly larger than 1, then roughly speaking the limiting averaged empirical distribution has all moments.