Ralaivaosaona, Dimbinaina
[Verfasser:in];
Sileikis, Matas
[Verfasser:in];
Wagner, Stephan
[Verfasser:in]
;
Dimbinaina Ralaivaosaona and Matas Sileikis and Stephan Wagner
[Mitwirkende:r]
Asymptotic Normality of Almost Local Functionals in Conditioned Galton-Watson Trees
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Beschreibung:
An additive functional of a rooted tree is a functional that can be calculated recursively as the sum of the values of the functional over the branches, plus a certain toll function. Janson recently proved a central limit theorem for additive functionals of conditioned Galton-Watson trees under the assumption that the toll function is local, i.e. only depends on a fixed neighbourhood of the root. We extend his result to functionals that are almost local, thus covering a wider range of functionals. Our main result is illustrated by two explicit examples: the (logarithm of) the number of matchings, and a functional stemming from a tree reduction process that was studied by Hackl, Heuberger, Kropf, and Prodinger.