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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 by pruning Galton–Watson trees and an analogous process by pruning a critical or subcritical Galton–Watson tree conditioned to be infinite. Under a mild condition on offspring distributions, we show that the process run until its ascension time has a representation in terms of . A similar result was obtained by Aldous and...
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