Pruning and contraction on Galton-Watson and splitting trees

Talk at 1st annual meeting of the West Coast Coin Flippers Union. Abstract: Suppose each edge of a Galton-Watson (GW) tree has probability p of being marked for pruning. If we prune away the marked edges (which means also removing the subtree above each such edge), then the resulting tree remains a Galton-Watson tree, but with a new offspring distribution. This has been shown to generalize to Lévy trees, which are the continuum limits of GW trees. Of particular interest are the stable continuum random trees, which comprise