Exact Asymptotics for the Harmonic Descent Chain and Extended Convergence Bounds for Recursive Statistics

We give an exact asymptotic expansion of the occupation probabilities $a(n,k)$ of the harmonic descent chain, introduced by D. Aldous, as $n\rightarrow\infty$ with $k\in\mathrm{o}(\sqrt{n})$. In addition, we extend the recent results of Brandenberger et al. by giving a bound on the rate of convergen