A few years ago, Grimmett, Kesten and Zhang proved that for supercritical bond percolation on Z 3 , simple random walk on the innnite cluster is a.s. transient. We generalize this result to a class of wedges in Z 3 including, for any " 2 (0; 1), the wedge W " = f(x; y; z) 2 Z 3 : x 0; jzj x " g which can be thought of as representing a (2 + ")-dimensional lattice. Our proof builds on recent wor...

We apply percolation theory to a recently proposed measure of fragmentation F for social networks. The measure F is defined as the ratio between the number of pairs of nodes that are not connected in the fragmented network after removing a fraction q of nodes and the total number of pairs in the original fully connected network. We compare F with the traditional measure used in percolation theo...

Multifragment disintegration of finite systems with toroidal and bubble-shaped configurations is studied within the framework of a bond-percolation model. Calculations for these finite systems predict enhanced fragment production for less compact decay configurations. Power law fits to the predicted mass distributions reveal a strong sensitivity of the extracted critical exponents on the geomet...

We present conjectured exact expressions for two types of correlations in the dense O(n = 1) loop model on L×∞ square lattices with periodic boundary conditions. These are the probability that a point is surrounded by m loops and the probability that k consecutive points on a row are on the same or on different loops. The dense O(n = 1) loop model is equivalent to the bond percolation model at ...

We consider a spatial model related to bond percolation for the spread of a disease that includes variation in the susceptibility to infection. We work on a lattice with random bond strengths and show that with strong disorder, i.e. a wide range of variation of susceptibility, patchiness in the spread of the epidemic is very likely, and the criterion for epidemic outbreak depends strongly on th...