Localization and Propagation in Random Lattices

We analyze the motion of a particle on random lattices. Scatterers of two different types are independently distributed among the vertices of such a lattice. A particle hops from a vertex to one of its neighboring vertices. The choice of neighbor is completely determined by the type of scatterer at the current vertex. It is shown that on Poisson and vectorizable random triangular lattices the particle will either propagate along some unbounded strip or be trapped inside a closed strip. We also characterize the structure of a localization zone contained within a closed strip. Another result shows that for a general class of random lattices the orbit of a particle will be bounded with probability one.