Limit distribution of the degrees in scaled attachment random recursive trees

We study the limiting distribution of the degree of a given node in a scaled attachment random recursive tree, a generalized random recursive tree, which is introduced by Devroye et. al (2011). In a scaled attachment random recursive tree, every node i is attached to the node labeled [iX(i)] where X-0,, X-n is a sequence of i.i.d. random variables, with support in [0, 1) and distribution function F. By imposing a condition on F, we show that the degree of a given node is asymptotically normal.