|
Abstract:
|
Bootstrap percolation on a graph is a deterministic process that iteratively enlarges a set of occupied sites by adjoining points with at least theta occupied neighbours. In the polluted bootstap percolation model in Z^2, the vertices of Z^2 are independently declared occupied with probability p, closed with probability q and empty otherwise, where p+q < 1. For any x in Z^2, first its neighbourhood structure is defined appropriately. At any integer-valued time point t, an empty vertex gets occupied if at time t-1, it is empty and has theta occupied neighbours. Vertices which are already occupied or closed do not change state.Our objective is to study the final density of occupied sites as p,q -->0 and to see if there is any critical scaling relation between p and q which affects the probability that any vertex is eventually occupied.
|
