Percolation of three fluids on a honeycomb lattice

TL;DR

This paper details the proof that three-fluid percolation processes on a honeycomb lattice become independent at small scales and discusses related conjectures based on numerical experiments.

Contribution

It provides a detailed, simplified proof of mutual independence in three-fluid percolation on honeycomb lattices and introduces new conjectures from numerical data.

Findings

Percolation processes become mutually independent as lattice step approaches zero.

The paper offers a simplified proof accessible to nonspecialists.

Numerical experiments suggest new related conjectures.

Abstract

In this paper, we consider a generalization of percolation: percolation of three related fluids on a honeycomb lattice. K. Izyurov and A. Magazinov proved that percolations of distinct fluids between opposite sides on a fixed hexagon become mutually independent as the lattice step tends to 0. This paper exposes this proof in details (with minor simplifications) for nonspecialists. In addition, we state a few related conjectures based on numerical experiments.