Localization of the 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.
 Publication:

Physical Review Letters
 Pub Date:
 April 2009
 DOI:
 10.1103/PhysRevLett.102.160602
 arXiv:
 arXiv:0810.4113
 Bibcode:
 2009PhRvL.102p0602B
 Keywords:

 05.40.Fb;
 72.15.Rn;
 89.70.Cf;
 Random walks and Levy flights;
 Localization effects;
 Entropy and other measures of information;
 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Statistical Mechanics
 EPrint:
 4 pages, 3 figures, minor changes in the discussion at the end of the paper