Asymptotic cost of cutting down random free trees

TL;DR

This paper analyzes the asymptotic cost of randomly cutting free trees, revealing the limit distribution of total splitting cost using advanced generating function techniques and the method of moments.

Contribution

It introduces a novel approach to determine the asymptotic distribution of cutting costs in random free trees through generating function analysis.

Findings

Limit distribution characterized for total cutting cost

Asymptotic behavior linked to generating function properties

Method of moments applied to derive distribution results

Abstract

The limit distribution of the total cost incurred by splitting a tree uniformly distributed on the set of all finite free trees, appears as an additive functional induced by a toll equal to the square of the size of tree. The main tools used are the recent results connecting the asymptotics of generating functions with the asymptotics of their Hadamard product, and the method of moments.