Localization of maximal entropy random walk
I will 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, I will consider a lattice with weak dilution. I will 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, can be explained in terms of the Lifshitz states of a certain random operator. I will also show a connection of maximal entropy random walk with the Feynman formulation of Quantum Mechanics (so called path-integral approach) and shows that this new random walk leads to localization of particles in some discretizations of curved space-times.
This is a weekly series of informal talks given primarily by members of the soft condensed matter and statistical mechanics groups, but is also open to members of other groups and external visitors. The aim of the series is to promote discussion and learning of various topics at a level suitable to the broad background of the group. Everyone is welcome to attend..