Theoretical Statistics and Mathematics Unit, ISI 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).