A Conditioning Principle for Galton–watson Trees
نویسنده
چکیده
We show that an infinite Galton-Watson tree, conditioned on its martingale limit being smaller than ε, converges as ε ↓ 0 in law to the regular μ-ary tree, where μ is the essential minimum of the offspring distribution. This gives an example of entropic repulsion where the limit has no entropy.
منابع مشابه
A Note on Conditioned Galton-watson Trees
We give a necessary and sufficient condition for the convergence in distribution of a conditioned Galton-Watson tree to Kesten’s tree. This yields elementary proofs of Kesten’s result as well as other known results on local limit of conditioned Galton-Watson trees. We then apply this condition to get new results, in the critical and sub-critical cases, on the limit in distribution of a Galton-W...
متن کاملPruning Galton-Watson Trees and Tree-valued Markov Processes
Abstract. We present a new pruning procedure on discrete trees by adding marks on the nodes of trees. This procedure allows us to construct and study a tree-valued Markov process {G(u)} by pruning Galton-Watson trees and an analogous process {G(u)} by pruning a critical or subcritical Galton-Watson tree conditioned to be infinite. Under a mild condition on offspring distributions, we show that ...
متن کاملAn invariance principle for random planar maps
We show a new invariance principle for the radius and other functionals of a class of conditioned ‘Boltzmann-Gibbs’distributed random planar maps. It improves over the more restrictive case of bipartite maps that was discussed in Marckert and Miermont (2006). As in the latter paper, we make use of a bijection between planar maps and a class of labelled multitype trees, due to Bouttier et al. (2...
متن کاملThe lineage process in Galton-Watson trees and globally centered discrete snakes
We consider branching random walks built on Galton-Watson trees with offspring distribution having a bounded support, conditioned to have n nodes, and their rescaled convergences to the Brownian snake. We exhibit a notion of “globally centered discrete snake” that extends the usual settings in which the displacements are supposed centered. We show that under some additional moment conditions, w...
متن کاملA note on the probability of cutting a Galton-Watson tree
The structure of Galton-Watson trees conditioned to be of a given size is wellunderstood. We provide yet another embedding theorem that permits us to obtain asymptotic probabilities of events that are determined by what happens near the root of these trees. As an example, we derive the probability that a Galton-Watson tree is cut when each node is independently removed with probability p, where...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010