Dynamics of Maximal Entropy Random Walk and Generic Random Walk on Cayley Trees
Dynamics of Maximal Entropy Random Walk and Generic Random Walk on Cayley Trees
This Demonstration compares the relaxation of probability distributions to the stationary state for a generic random walk (GRW) and a maximal entropy random walk (MERW) on a Cayley tree. For GRW a particle chooses one of the neighboring sites with equal probability, while for MERW the particle moves in such a way that all trajectories of a given length between two given points are equiprobable.
The area of nodes in the plot as well as their color corresponds to the probability of finding a particle performing a random walk in the given node (the brighter the color, the higher the probability). The logarithmic plot on the right shows how much the probability measured at the red-circled point differs from the probability reached after infinite time (so-called stationary state). You can change the choice of the two initial points (the dash-circled vertices) together with their probabilities.