Quenched local convergence of Boltzmann planar maps

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.

The results of this work were initially part of [21]. The paper got split during the refereeing process following a referee's recommendation. arXiv admin note: substantial text overlap with arXiv:1908.04843