Non-backtracking Random Walk

We consider non-backtracking random walk (NBW) in the nearest-neighbor setting on the ? ^d -lattice and on tori. We evaluate the eigensystem of the m×m-dimensional transition matrix of NBW where m denote the degree of the graph. We use its eigensystem to show a functional central limit theorem for NBW on ? ^d and to obtain estimates on the convergence towards the stationary distribution for NBW on the torus.