Forests on wired regular trees

TL;DR

This paper studies the arboreal gas model on a wired regular tree, providing a detailed description of its weak limit, which enhances understanding of forest configurations in percolation models.

Contribution

It offers the first comprehensive analysis of the arboreal gas on a wired regular tree, characterizing its weak limit and behavior.

Findings

Describes the weak limit of the arboreal gas on wired regular trees.

Provides insights into forest structures in percolation models.

Enhances understanding of conditioned percolation processes.

Abstract

The Arboreal gas model on a finite graph $G$ is the Bernoulli bond percolation on $G$ conditioned on the event that the sampled subgraph is a forest. In this short note we study the arboreal gas on a regular tree wired at the leaves and obtain a comprehensive description of the weak limit of this model.