Abstract
The degree profile in a random planted plane tree was considered. For any d≥1, it was proven that under suitable normalization, the number of vertices of degree d in a random planted plane tree with n edges has asymptotic normality, as n goes to infinity. The asymptotic formulae for the expectation and variance of this random variable were also given. An analytical method was employed in the proof.
Abstract
The degree profile in a random planted plane tree was considered. For any d≥1, it was proven that under suitable normalization, the number of vertices of degree d in a random planted plane tree with n edges has asymptotic normality, as n goes to infinity. The asymptotic formulae for the expectation and variance of this random variable were also given. An analytical method was employed in the proof.