  Strongly non-Markovian random walks offer a promising modeling framework for
understanding animal and human mobility, yet, few analytical results are
available for these processes. Here we solve exactly a model with long range
memory where a random walker intermittently revisits previously visited sites
according to a reinforced rule. The emergence of frequently visited locations
generates very slow diffusion, logarithmic in time, whereas the walker
probability density tends to a Gaussian. This scaling form does not emerge from
the Central Limit Theorem but from an unusual balance between random and
long-range memory steps. In single trajectories, occupation patterns are
heterogeneous and have a scale-free structure. The model exhibits good
agreement with data of free-ranging capuchin monkeys.
