Constrained Random Walk of a carrier in two-dimensional site-percolation lattice, exemplified by virtual and real world scenarios

A Random Walk (RW) realization in the square lattice, upon which a percolation cluster of sites, visited one by one by random walkers is built up (by direct Monte Carlo method), has been carried out towards its basic tendencies. It turns out that if the RW is realized near the site-percolation threshold, the process, as expected, decelerates. If, in turn, one systematically goes above the percolation threshold, being roughly about 0.6, towards the isotropic site-cluster regime, the process accelerates. Some drift superimposed on the RW realization as well as boundary conditions of certain types change the system behavior in a quite predictive way. Both new and interesting examples, emphasizing a possible applications of the phenomenon under study, are carefully mentioned. A finite-size effect always incorporated in the realized MC-algorithm is going to make the process apparently closer to reality. The notion of continuous phase (sub)transition has been discussed in the presented context.