Year: 2026
Type: preprint
Abstract: We show that the percolation components on a square grid can be $5$-colored as a factor of iid so that neighboring components get different colors. Above the critical probability, we observe that these regions can be 4-colored. Along the way, we extend the classical correspondence between fiid process and measurable labellings of the Bernoulli shift to this quotient setting, prove a general coloring result about hyperfinite pmp planar graphs, and clarify some foundational issues about how to define planarity for Borel graphs.
Source: arXiv (Cornell University)
Authors: Hsu, Justin, Sium, Daniel, Thornton, Riley
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214702793