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 percolat ion 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 tendenci es. It turns out that if the RW is realized near the site-percolation thres hold, the process, as expected, decelerates. If, in turn, one systematicall y goes above the percolation threshold, being roughly about 0.6, towards th e isotropic site-cluster regime, the process accelerates. Some drift superi mposed on the RW realization as well as boundary conditions of certain type s change the system behavior in a quite predictive way. Both new and intere sting examples, emphasizing a possible applications of the phenomenon under study, are carefully mentioned. A finite-size effect always incorporated i n the realized MC-algorithm is going to make the process apparently closer to reality. The notion of continuous phase (sub)transition has been discuss ed in the presented context.