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Limit theorems for conditioned non-generic Galton-Watson trees · Around

2012

Limit theorems for conditioned non-generic Galton-Watson trees

Kortchemski, Igor

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We study a particular type of subcritical Galton--Watson trees, which are called non-generic trees in the physics community.

In contrast with the critical or supercritical case, it is known that condensation appears in certain large conditioned non-generic trees, meaning that with high probability there exists a unique vertex with macroscopic degree comparable to the total size of the tree.
Using recent results concerning subexponential distributions, we investigate this phenomenon by studying scaling limits of such trees and show that the situation is completely different from the critical case.
In particular, the height of such trees grows logarithmically in their size.

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