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Conditioned multi-type Galton-Watson trees

Authors
  • Cator, Eric
  • Don, Henk
Type
Preprint
Publication Date
Jul 22, 2015
Submission Date
Jun 08, 2015
Identifiers
arXiv ID: 1506.02610
Source
arXiv
License
Yellow
External links

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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