Orateur
Description
We consider critical percolation on a supercritical Galton- Watson tree with mean offspring m > 1. It is well known that the critical percolation probability for this model is 1/m and that the root cluster has the distribution of a critical Galton-Watson tree. For this reason, many properties of the cluster are well understood, such as aymptotics for long range survival probabilities, the size of the n-th generation conditioned on survival (the “Yaglom limit”), and convergence of the entire cluster to a branching process/stable tree. All of these results as stated are annealed, that is, we take the expectation with respect to the distribution of the tree and the percolation configuration simultaneously. The goal of this talk is to consider the quenched regime: are the same properties true for almost any realisation of the tree? We will see that this is indeed the case, although some scaling constants will depend on the tree.
Based on joint works with Quirin Vogel and Tanguy Lions
