We consider non-backtracking random walk (NBW) in the nearest-neighbor setting on the Z 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 Z d and to obtain estimates on the convergence towards the stationary distribution for NBW on the torus.
|Journal||Journal of Statistical Physics|
|Publication status||Published - 2013|