| Event Title: | Random Oriented Trees - a model for drainage networks |
| Speaker: | Prof. Anish Sarkar |
| Affiliation: | Stat-Math Unit, Indian Statistical Institute, Delhi. |
| Abstract/Brief Description: | 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 $ v$ is connected by an edge to the closest open vertex $ w$ such that the $d$th co-ordinates of $ v$ and $ w$ satisfy ${w}(d) = v(d) -1$. In case of non-uniqueness of such a vertex $w$, we choose any one of the closest vertices with equal probability and independently of the other random mechanisms. It is shown that this random graph is a tree almost surely for $d=2$ and $3$ and it is an infinite collection of distinct trees for $d \geq 4$. In addition, for any dimension, we show that there is no bi-infinite path in the tree. |
| Subject Area: | Mathematics |
| Date: | Thursday, May 20, 2004 |
| Time: | 4:00pm-5:00pm |
| Duration: | 60 minutes |
| Venue: | Lecture Hall - I Dept. of Mathematics |