Random Walks on Finite Lattice Tubes

Abstract

Random walks from a single source on a finite element lattice were considered. Explicit formulas were derived for the absorption probabilities at the ends and for the expectations that a random walk will visit a particular lattice site before being absorbed. Results were presented for the triangular lattice tubes and the honeycomb lattice tubes model diffusion of adatoms on single walled zig-zag carbon nanotubes with open ends.