Elephant random walks; a review

Abstract. In the simple random walk the steps are independent, whereas in the elephant random walk (ERW), which was introduced by Schütz and Trimper in 2004 [33], the next step always depends on the whole path so far. In a series of earlier papers we have investigated some variations and extensions, in particular cases when the elephant has a restricted memory. In the present paper we summarize and extend some results on elephant random walks, closing with some remarks and open questions.