Zdzislaw Burda (Krakow):
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.
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