Year: 2026
Type: preprint
Abstract: For any fixed number $k\ge3$ of independent volume-sampled sites in the unit-area Brownian map, we represent the negative-power transform of their ordinary Voronoi volumes as a finite sum of marked planar scheme integrals. These integrals arise from the critical asymptotics of generating functions for face-constrained labelled planar maps. To connect them to Voronoi volumes, we use Miermont's zero-delay correspondence to interpret the labelled maps as quadrangulations with distinguished sites and then pass to the Brownian map scaling limit.
Source: arXiv (Cornell University)
Author: Sun, Zhenyao
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G620304959
OpenAlex ID: W7223964209