A central limit theorem for additive functionals of increasing trees. (8th March 2019) - Ralaivaosaona, Dimbinaina; Wagner, Stephan
Abstract: A tree functional is called additive if it satisfies a recursion of the form F(T) = _j=1^k F(B_j) + f(T), where B 1, …, Bk 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 toll 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.