A note on the limit law of one-sided tree destruction

TL;DR

This paper identifies the limit law of one-sided tree destruction with a toll function as the local time of a noise reinforced Bessel process, building on previous work by Fill, Kapur, and Panholzer.

Contribution

It provides a new characterization of the limit law using recent stochastic process results, extending prior moment-based findings.

Findings

Limit law expressed as local time of a noise reinforced Bessel process

Connects tree destruction limit law to stochastic process theory

Builds on recent advances by Bertoin (2022)

Abstract

This short note serves an addendum to the article "Destruction of very simple trees" by Fill, Kapur and Panholzer (2004). Therein, the limit law of one-sided tree destruction with a toll function was determined by its moment sequence. We add an identification of the limit law, using recent results of Bertoin (2022), in terms of the local time of a noise reinforced Bessel process.