Anti-persistent correlated random walks

An analysis is presented of anti-persistent random walks, in which after any step there is an increased probability of returning to the original site. In addition to their intrinsic interest in the theory of random walks, they are relevant to certain problems in hopping transport, such as ionic conduction. An analysis is presented of such walks on hypercubic lattices in an arbitrary number of dimensions, for both discrete time and continuous time random walks, and exact formulae are derived for the mean square distance travelled in n steps or in time t. The relevance of these results to the observed frequency dependence of ionic conductivity is discussed.