30 citations · 54 across the 3 of their papers we have counts for
9 papers
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…
The k-core and branching processes
Oliver Riordan
The k-core of a graph G is the maximal subgraph of G having minimum degree at least k. In 1996, Pittel, Spencer and Wormald found the threshold for the emergence of a non-tri…
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…