Penalization of Galton Watson trees with marked vertices

2024/03/01 by Abraham, Romain, Boulal, Sonia, Debs, Pierre
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2403.00384

Abstract

We consider a Galton-Watson tree where each node is marked independently of each others with a probability depending on itsout-degree. Using a penalization method, we exhibit new martingales where the number of marks up to level n -- 1 appears. Then, we use these martingales to define new probability measures via a Girsanov transformation and describe the distribution of the random trees under these new probabilities.

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