# Seminar at SMU Delhi

August 1, 2012 (Wednesday) , 3:30 PM at Webinar
Speaker: Kumarjit Saha, Indian Statistical Institute, Delhi
Title: Directed Spanning Forest and Brownian web
Abstract of Talk
Consider the $d$ dimensional lattice ${\mathbb Z}^d$ where each vertex is open' or closed' with probability $p$ or $1-p$ respectively. An open vertex $\mathbf{v} := (\mathbf{v}(1), \mathbf{v}(2), \ldots, \mathbf{v}(d))$ is connected by an edge to another open vertex $\bw$, which has the minimum $L_1$ distance among all the open vertices $\bx$ with $\mathbf{x}(d)>\mathbf{v}(d)$. It is shown that this random graph is a tree almost surely for $d=2$ and $3$ and it is an infinite collection of disjoint trees for $d\geq 4$. In addition, for $d=2$, we show that when aprropriately scaled, family of its paths converges in distribution to the Brownian web.