Tree-valued Markov Chains Derived from Galton-watson Processes
نویسنده
چکیده
Let G be a Galton-Watson tree, and for 0 u 1 let Gu be the subtree of G obtained by retaining each edge with probability u. We study the tree-valued Markov process (Gu; 0 u 1) and an analogous process (G u; 0 u 1) in which G 1 is a critical or subcritical Galton-Watson tree conditioned to be in nite. Results simplify and are further developed in the special case of Poisson( ) o spring distribution. Running head. Tree-valued Markov chains.
منابع مشابه
Tree-valued Markov chains and Poisson-Galton-Watson distributions
The Poisson-Galton-Watson distribution on nite trees, and the related PGW 1 (1) distribution on innnite trees with one end, arise in several contexts, in particular as n ! 1 weak limits within various size-n combinato-rial models. We review this topic, introducingslick notation for describing such distributions. We then describe a family of continuous-time Markov chains whose marginal distribut...
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 کاملInvited Talks
Bénédicte Haas, University of Paris-Dauphine, France Limits of Non-increasing Markov Chains and Applications to Random Trees and Coalescents Consider a non-increasing Markov chain with values in the set of non-negative integers, starting from a large integer !. We describe its scaling limit as ! → ∞, under the assumption that the large jump events are rare and happen at rates that behave like a...
متن کاملA symmetric entropy bound on the non-reconstruction regime of Markov chains on Galton-Watson trees
We give a criterion of the form Q(d)c(M) < 1 for the non-reconstructability of tree-indexed q-state Markov chains obtained by broadcasting a signal from the root with a given transition matrix M . Here c(M) is an explicit constant defined in terms of a q − 1-dimensional variational problem over symmetric entropies, and Q(d) is the expected number of offspring on the Galton-Watson tree. This res...
متن کاملBranching Processes in Stochastic Environments
This paper is concerned with two simple models for branching processes in stochastic environments. The models are identical to the model for the classical Galton-Watson branching process in all respects but one. In the family-tree language commonly used to describe branching processes, that difference is that the probability distribution for the number of offspring of an object changes stochast...
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 1997