Scaling limits of Markov branching trees and Galton-Watson trees   conditioned on the number of vertices with out-degree in a given set
  We generalize recent results of Haas and Miermont to obtain scaling limits of Markov branching trees whose size is specified by the number of nodes whose out-degree lies in a given set. We then show that this implies that the scaling limit of finite variance Galton-Watson trees condition on the number of nodes whose out-degree lies in a given set is the Brownian continuum random tree. The key to this is a generalization of the classical Otter-Dwass formula. 
Douglas Rizzolo
math.PR