Generic Random Walk and Maximal Entropy Random Walk
Generic Random Walk and Maximal Entropy Random Walk
The plots compare the stationary probability of finding a particle performing a random walk on a 2D square lattice with randomly distributed defects for Generic Random Walk (GRW) and Maximal Entropy Random Walk (MERW). The darker a region, the lower the stationary probability of finding a particle there. For GRW the particle chooses one of the neighboring sites with equal probability, while for MERW the particle moves in such a way that all trajectories of given length between two given points are equiprobable. By changing the density of defects, that is, of randomly erased links (marked in red in the plot), you can observe that for GRW the probability spans the whole lattice while for MERW it is localized in the largest region free of defects.