Simply generated trees,B‐series and Wigner processes

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 semi‐circular elements. © 2004 Wiley Periodicals, Inc. Random Struct. Alg. 2004