Anomalous diffusion at percolation threshold in high dimensions on 10(18) sites
Using an inverse of the standard linear congruential random number generator, large randomly occupied lattices can be visited by a random walker without having to determine the occupation status of every lattice site in advance. In seven dimensions, at the percolation threshold with L-7 sites and L less than or equal to 420, we confirm the expected time-dependence of the end-to-end distance (including the corrections to the asymptotic behavior).
anomalous diffusion random number generators monte carlo ant in labyrinth