  We consider non-backtracking random walk (NBW) in the nearest-neighbor
setting on the Zd-lattice and on tori. We evaluate the eigensystem of the m X
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 Zd
and to obtain estimates on the convergence towards the stationary distribution
for NBW on the torus.
