Conditioned multi-type Galton-Watson trees

Eric Cator; Henk Don

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arXiv · 1506.02610

Conditioned multi-type Galton-Watson trees

Eric Cator·Henk Don

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Abstract

We consider multi-type Galton Watson trees, and find the distribution of these trees when conditioning on very general types of recursive events. It turns out that the conditioned tree is again a multi-type Galton Watson tree, possibly with more types and with offspring distributions, depending on the type of the father node and on the height of the father node. These distributions are given explicitly. We give some interesting examples for the kind of conditioning we can handle, showing that our methods have a wide range of applications.

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Eric Cator, Henk Don. 2015-06-08. Conditioned multi-type Galton-Watson trees. https://arxiv.org/abs/1506.02610

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