Stationary States of Maximal Entropy Random Walk and Generic Random Walk on Cayley Trees
Stationary States of Maximal Entropy Random Walk and Generic Random Walk on Cayley Trees
This Demonstration compares the stationary probabilities of a generic random walk (GRW) and a maximal entropy random walk (MERW) on a Cayley tree. 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 a given length between two given points are equiprobable.
The area of nodes in the plot as well as their color is proportional to the probability of finding a particle performing a random walk in the given node (the brighter the color, the higher the probability). The plot on the right shows the probabilities as a function of the distance from the center, either as a probability for a given node or as a probability summed over a whole generation of nodes (all nodes equidistant from the center). The limiting probability distributions are theoretical curves corresponding to a tree with an infinite number of generations.