30 citations · 54 across the 3 of their papers we have counts for
Showing 2004 · math.PRShow all
3 papers · 2 filters
math.PR2004
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…
math.PR2004
A short proof of the Harris-Kesten Theorem
Bela Bollobas, Oliver Riordan
We give a short proof of the fundamental result that the critical probability for bond percolation in the planar square lattice is equal to 1/2. The lower bound was proved by Harri…
math.PR2004
The critical probability for random Voronoi percolation in the plane is 1/2
Bela Bollobas, Oliver Riordan
We study percolation in the following random environment: let be a Poisson process of constant intensity in the plane, and form the Voronoi tessellation of the plane with respe…