Strongly non-Markovian random walks offer a promising modeling framework for
understanding animal and human mobility, yet, few analytical results are available for these …

The purpose of this paper is to establish, via a martingale approach, some refinements on
the asymptotic behavior of the one-dimensional elephant random walk (ERW). The …

Elephant random walk is a kind of one-dimensional discrete-time random walk with infinite
memory: For each step, with probability α α the walker adopts one of his/her previous steps …

We present a random walk model that exhibits asymptotic subdiffusive, diffusive, or
superdiffusive behavior in different parameter regimes. This appears to be an instance of a …

One class of random walks with infinite memory, so-called elephant random walks, are
simple models describing anomalous diffusion. We present a surprising connection between …

The purpose of this paper is to investigate the asymptotic behavior of the multi-dimensional
elephant random walk (MERW). It is a non-Markovian random walk which has a complete …

We study the elephant random walk in arbitrary dimension $ d\geq 1$. Our main focus is the
limiting random variable appearing in the superdiffusive regime. Building on a link between …

Motivated by studies on the recurrent properties of animal and human mobility, we introduce
a path-dependent random-walk model with long-range memory for which not only the mean …

For almost a decade the consensus has held that the random walk propagator for the
elephant random walk (ERW) model is a Gaussian. Here we present strong numerical …

In the classical simple random walk the steps are independent, that is, the walker has no
memory. In contrast, in the elephant random walk, which was introduced by Schütz and …