Localization of the Maximal Entropy Random Walk
2009; American Physical Society; Volume: 102; Issue: 16 Linguagem: Inglês
10.1103/physrevlett.102.160602
ISSN1092-0145
AutoresZ. Burda, Jarosław Duda, J. M. Luck, Bartłomiej Wacław,
Tópico(s)Mathematical Dynamics and Fractals
ResumoWe 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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