# Seminar at SMU Delhi

September 26, 2012 (Wednesday) , 3:30 PM at Webinar
Speaker: Ghurumuruhan Ganesan, Indian Statistical Institute, Delhi
Title: Size of Giant Component and Infection Spread in Random Geometric Graphs
Abstract of Talk
Consider $n$ nodes independently and uniformly distributed in the unit square $S$ centred at origin. Connect two nodes by an edge if the distance between them is less than $r_n,$ where $nr_n^2 \longrightarrow \infty$ and $nr_n^2 \leq A\log{n}$ for some constant $A.$ The resulting graph $G$ is called the random geometric graph. In the first part of the talk, we show that the giant component of $G$ contains at least $n - o(n)$ nodes with probability at least $1 - o(1).$ In the second part of the talk, we study infection spread in $G.$ We prove that the infection spreads with speed at least $D_1nr_n^2$ and at most $D_2nr_n^2$ for some positive constants~$D_1$ and~$D_2.$ This is unlike infection spread in regular graphs (like e.g. $\mathbb{Z}^2$) where infection spreads at a constant speed. Reference: G. Ganesan. (2012). Size of the Giant Component in a Random Geometric Graph. Accepted for Publ. in Ann. Inst. Henri Poin.