Simply generated trees, B-series and Wigner processes

Authors:
Christian Mazza
Affiliations:
Section de Mathématiques, 2-4 Rue du Lièvre, CP 240, CH-1211 Genève 24, Switzerland
Venue:
Random Structures & Algorithms
Year:
2004

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Abstract

We consider simply generated trees, like rooted plane trees, and consider the problem of computing generating functions of so-called bare functionals, like the tree factorial, using B-series from Butcher's theory. We exhibit a special class of functionals from probability theory: the associated generating functions can be seen as limiting traces of product of semicircular elements.