The maximum entropy random walk in a disordered lattice is obtained as a consequence of the principle of maximum entropy for a particular type of prior information without restriction on the number of steps. This novel result demonstrates that transition probabilities defining the random walk represent a general characterization of information on a defective lattice and does not necessarily reflect a physical process. The localization phenomenon is shown to be a consequence of solution of the Laplacian on the lattice—hence it contradicts the previous interpretation as a spherical Lifshitz state—and naturally generalizes to multiple modes, whose order reflects the significance of information. The dynamics of information flow on the microscale is related to the macroscopic structure of the lattice through a Fokker-Planck formalism. This newly derived theoretical framework is opening doors for a wide range of applications in analysis of (information) flow in disordered systems. That includes potentially breakthrough resolution of the outstanding problem of inferring connectivity from discrete imaging (i.e., neural) data.

• Received 15 August 2013
• Revised 11 October 2013

DOI:https://doi.org/10.1103/PhysRevE.89.032142