Mean first-passage time of random walks on a random lattice

Abstract

The mean first-passage time (MFPT) of random walks on one-dimensional disordered lattice segments is considered. Disorder is modeled by prescribing random transition and sojourn probabilities to the lattice sites. We consider several models of disorder: models with symmetric and asymmetric random transition probabilities, random sojourn probabilities, and models with bond randomness. For these models we present exact results on the MFPT and disorder-averaged MFPT. We do not find any anomalous dependence of the disorder-averaged MFPT on the size of the lattice segment. The distribution of the MFPT resulting from the disorder is Gaussian for the models with symmetric and site symmetric transition probabilities and non-Gaussian for models with asymmetric transition probabilities.