Bootstrap percolation, a model of irreversible activation on graphs, has emerged as a pivotal area within graph theory and statistical mechanics. In this process, nodes (or vertices) on a network are ...

The Annals of Applied Probability, Vol. 22, No. 5 (October 2012), pp. 1989-2047 (59 pages) Bootstrap percolation on the random graph G n,p is a process of spread of "activation" on a given realization ...

We consider a version of continuum long-range percolation on finite boxes of ℝd in which the vertex set is given by the points of a Poisson point process and each pair of two vertices at distance r is ...

In 2008, the mathematician Oded Schramm died in a hiking accident in the Cascade mountains some 50 miles east of Seattle. Though he was just 46 years old, he had constructed entirely new areas of ...