A central limit theorem for additive functionals of increasing trees

A tree functional is called additive if it satisfies a recursion of the form F(T) = Sigma(k)(j=1) F(B-j) + f(T), where B-1, ..., B-k are the branches of the tree T and f(T) is a toll function. We prove a general central limit theorem for additive functionals of d-ary increasing trees under suitable assumptions on the loll function. The same method also applies to generalized plane-oriented increasing trees (GPORTs). One of our main applications is a log-normal law that we prove for the size of the automorphism group of d-ary increasing trees, but other examples (old and new) are covered as well.