Number of maximal rooted trees in uniform attachment model via stochastic approximation

We study the asymptotic behavior of the number of maximal trees in a uniform attachment model. In our model, we consider a sequence of graphs built by the following recursive rule. We start with the complete graph on $m+1$ vertices, $m>1$. Then on the $n+1$ step, we add vertex $n+1$ and draw $m$ edges from it to different vertices, chosen uniformly from $1,\ldots,n$. We prove the convergence speed for the number of maximal trees in such a model using the stochastic approximation technique.