Seminar at SMU Delhi

April 6, 2011 (Wednesday) , 3:30 PM at Webinar
Speaker: Ghurumuruhan Ganesan, Indian Statistical Institute, Delhi
Title: Critical Probabilities of bond percolation in Delaunay triangulation and Voronoi tessellation
Abstract of Talk
We consider bond percolation with parameter p on the Delaunay Triangulation (DT) generated by a Poisson point process of unit intensity in $R^2.$ Let $p_c$ and $p^*_c,$ respectively, denote the critical probabilities for the bond percolation in DT and its dual, the Voronoi Tessellation (VT). In many regular lattices, we know that $p_c + p^*_c = 1 (1).$ In random lattices, very few exact critical probabilities have been established. For the Voronoi site percolation, Bollobas and Riordan (2006) have recently shown that the critical probability is 1/2. Using a crucial RSW result of Bollobas and Riordan (2006), we prove that bond percolation in DT and VT satisfy (1).