30 citations · 54 across the 3 of their papers we have counts for
8 papers · 1 filter
Rigorous confidence intervals for critical probabilities
Oliver Riordan, Mark Walters
We use the method of Balister, Bollobas and Walters to give rigorous 99.9999% confidence intervals for the critical probabilities for site and bond percolation on the 11 Archimedea…
Line-of-sight percolation
Bela Bollobas, Svante Janson, Oliver Riordan
Given , let be the graph with vertex set in which two vertices are joined if they agree in one coordinate and differ by at most in the other. (Thus $Z…
Percolation on dual lattices with k-fold symmetry
Bela Bollobas, Oliver Riordan
Zhang found a simple, elegant argument deducing the non-existence of an infinite open cluster in certain lattice percolation models (for example, p=1/2 bond percolation on the squa…
A note on the Harris-Kesten Theorem
Bela Bollobas, Oliver Riordan
Recently, a short proof of the Harris-Kesten result that the critical probability for bond percolation in the planar square lattice is 1/2 was given, using a sharp threshold result…
Spread-out percolation in R^d
Bela Bollobas, Svante Janson, Oliver Riordan
Let be either or the points of a Poisson process in of intensity 1. Given parameters and , join each pair of points of within distance independently…
Sharp thresholds and percolation in the plane
Bela Bollobas, Oliver Riordan
Recently, the authors showed that the critical probability for random Voronoi percolation in the plane is 1/2. A by-product of the method was a short proof of the Harris-Kesten The…