Pruning, cut trees, and the reconstruction problem

TL;DR

This paper introduces a novel approach to the reconstruction problem for inhomogeneous continuum random trees, including pruning and cut trees, which extends previous methods limited to Brownian and stable trees.

Contribution

It presents a new, more general method for the reconstruction problem that does not depend on self-similarity, applicable to a broader class of Le9vy trees.

Findings

New approach to the reconstruction problem for inhomogeneous CRTs

Applicable to general Le9vy trees, beyond Brownian and stable cases

Potentially broadens understanding of genealogical structures in random trees

Abstract

We consider a pruning of the inhomogeneous continuum random trees, as well as the cut trees that encode the genealogies of the fragmentations that come with the pruning. We propose a new approach to the reconstruction problem, which has been treated for the Brownian CRT in [Electron. J. Probab. vol. 22, 2017] and for the stable trees in [Ann. IHP B, vol 55, 2019]. Our approach does not rely upon self-similarity and can potentially apply to general L\'evy trees as well.