# Seminar at SMU Delhi

April 1, 2015 (Wednesday) , 3:30 PM at Webinar
Speaker: Kumarjit Saha, Indian Statistical Institute, Delhi
Title: Directed spanning forest
Abstract of Talk
The directed spanning forest(DSF) was introduced by Baccelli and Bordenave. Consider a homogeneous Poisson point process ${\cal N}$ on $\mathbb{R}^d$. The DSF on $\mathbb{R}^d$ with direction $e_d$ is the random graph with vertex set ${\cal N}$ and edge set $E = \{: u \in {\cal N}\}$ where $h(u)$ is the nearest point in ${\cal N}$ to $u$ having strictly larger $d$ th co-ordinate. Coupier and Tran showed that for $d=2$, DSF consists of a single tree almost surely. We show that for $d=2,3$, DSF consists of a single tree nad for $d\geq 4$, DSF is a forest with infinitely many disjoint trees almost surely. This is a joint work with David Coupier, Anish Sarkar and Viet Chi Tran.