In this talk we will present some old and recent results on local limits for Galton-Watson trees conditioned to be large.
We shall first define the notion of local limit of discrete trees, recall the definition of Galton-Watson trees. We will introduce the Kesten’s tree which is a random tree with an infinite spine and give an elementary characterization for conditioned critical Galton-Watson trees to converge to the Kesten’s tree. The picture for sub-critical Galton-Watson trees is more delicate as some condensation phenomenon can appear. If time permits, we shall present other possible limits related to uniformly chosen trees with an exponential weight given by its height.