Localization of the maximal entropy random walk.

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 year

  2008

• Venue

  Physical Review Letters

• Publication date

  2008-10-22

• Fields of study

  Medicine, Physics

• Identifiers
  DOI 10.1103/PhysRevLett.102.160602arXiv 0810.4113PMID 19518691
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

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