RANDOM-WALKS ON KEBAB LATTICES - LOGARITHMIC DIFFUSION ON ORDERED STRUCTURES

Kebab lattices are ordered lattices obtained matching an infinite two- dimensional lattice to each point of a linear chain. Discrete time ran dom walks on these structures are studied by analytical techniques. Th e exact asymptotic expressions of the mean square displacement and of the RW Green functions show an unexpected logarithmic behavior that is the first example of such kind of law on an ordered structure. Moreov er the probability of returning to the origin shows the fastest long t ime decay ever found for recursive random walks.