Abstract
Let G be a Galton-Watson tree, and for 0 ≤ u ≤ 1 let G u be the subtree of G obtained by retaining each edge with probability u. We study the tree-valued Markov process ( G u , 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 infinite. Results simplify and are further developed in the special case of Poisson offspring distribution.
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