Localization of maximal entropy random walk

Abstract

We define a new class of random walk processes which maximize entropy. This maximal entropy random walk is equivalent to generic random walk if it takes place on a regular lattice, but it is not if the underlying lattice is irregular. In particular, we consider a lattice with weak dilution. We show that the stationary probability of finding a particle performing maximal entropy random walk localizes in the largest nearly spherical region of the lattice which is free of defects. This localization phenomenon, which is purely classical in nature, is explained in terms of the Lifshitz states of a certain random operator.

4 pages, 3 figures, minor changes in the discussion at the end of the paper

References in corpus (5)

• Glassy dynamics of kinetically constrained models
• Spectral Dimension of the Universe
• Universal Record Statistics of Random Walks and Lévy Flights
• Critical scaling in standard biased random walks
• Random Walks on Complex Networks

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