Other versions available
Percolation of sites not removed by a random walker in d dimensions
Abstract: How does removal of sites by a random walk lead to blockage of percolation? To study this problem of correlated site percolation, we consider a random walk (RW) of steps on a -dimensional hypercubic lattice of size (with periodic boundaries). We systematically explore dependence of the probability of percolation (existence of a spanning cluster) of sites not removed by the RW on and . The concentration of unvisited sites decays exponentially with increasing , while the visited sites are highly correlated—their correlations decaying with the distance as (in ). On increasing , the percolation probability approaches a step function, jumping from 1 to 0 when crosses a percolation threshold that is close to 3 for all . Within numerical accuracy, the correlation length associated with percolation diverges with exponents consistent with . There is no percolation threshold at the lower critical dimension of , with the percolation probability approaching a smooth function .
Keywords: function / percolation / threshold / walk / sites not removed / dimension / step
Scifeed alert for new publicationsNever miss any articles matching your research from any publisher
- Get alerts for new papers matching your research
- Find out the new papers from selected authors
- Updated daily for 49'000+ journals and 6000+ publishers
- Define your Scifeed now
Click here to see the statistics on "Physical Review E" .