After a brief introduction on the notion of amenability for groups, I will focus on the group of interval exchanges (the IET group) which is believed to be amenable. One of the (many) equivalent criteria to show that a group is amenable is Kesten's criterion on the return probabilities of random walks. In the case of G=IET, a recent work by Juschenko, Matte Bon, Monod and De La Salle provides a new criterion which is also of probabilistic nature. This new criterion involves the size of the inverted orbit of a certain random walk on the wobbling group $W(\mathbb{Z}^d)$ of permutations of $\mathbb{Z}^d$. The aim of this talk will be to introduce natural models of random walks on permutations of $\mathbb{Z}^d$ for which this criterion can be analyzed. The talk will not require any prerequisites.