Quenched local convergence of Boltzmann planar maps

TL;DR

This paper proves a quenched local convergence result for large Boltzmann planar maps, extending previous annealed convergence results by leveraging rerooted multi-type branching trees.

Contribution

It introduces a quenched convergence framework for Boltzmann planar maps, advancing understanding of their local structure in probabilistic combinatorics.

Findings

Establishes quenched local convergence of Boltzmann planar maps.

Extends annealed convergence results to a quenched setting.

Utilizes rerooted multi-type branching trees in the proof.

Abstract

Stephenson~(2018) established annealed local convergence of Boltzmann planar maps conditioned to be large. The present work uses results on rerooted multi-type branching trees to prove a quenched version of this limit.