Backbone and elastic backbone of percolation clusters obtained by the new method of 'burning'

Abstract

The authors introduce a method of obtaining information about percolation clusters in which the clusters are 'burned' in different ways. This method yields the backbone and the elastic backbone, their number of loops, shortest path and other quantities. It works in any dimension and can be applied also to other clusters. They obtain accurate estimates for the backbone exponents in two and three dimensions.