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- W2193024513 abstract "Crump-Mode-Jagers (CMJ) trees generalize Galton-Watson trees by allowing individuals to live for an arbitrary duration and give birth at arbitrary times during their life-time. In this paper, we are interested in the height and contour processes encoding a general CMJ tree. We show that the one-dimensional distribution of the height process can be expressed in terms of a random transformation of the ladder height process associated with the underlying Lukasiewicz path. As an application of this result, when edges of the tree are short we show that (1) the height process is obtained by stretching by a constant factor the height process of the associated genealogical Galton-Watson tree, and that (2) the contour process is obtained from the height process by a constant time change, thus generalizing a classical result in the Galton-Watson case." @default.
- W2193024513 created "2016-06-24" @default.
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- W2193024513 date "2015-06-10" @default.
- W2193024513 modified "2023-09-27" @default.
- W2193024513 title "Invariance principle for Crump-Mode-Jagers trees with short edges" @default.
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