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arXiv · 1412.5890

Constructing and searching conditioned Galton-Watson trees

Eric Cator·Henk Don
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Abstract

We investigate conditioning Galton-Watson trees on general recursive-type events, such as the event that the tree survives until a specific level. It turns out that the conditioned tree is again a type of Galton-Watson tree, with different types of offspring and a level-dependent offspring distribution, which will all be given explicitly. As an interesting application of these results, we will calculate the expected cost of searching a tree until reaching a given level.

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Eric Cator, Henk Don. 2014-12-18. Constructing and searching conditioned Galton-Watson trees. https://arxiv.org/abs/1412.5890

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