# Mixing time of Markov chains for the 1-2 model

## TL;DR

This paper introduces Markov chains for sampling 1-2 model configurations on hexagonal lattices and proves their mixing times are polynomial in graph size for many probability measures.

## Contribution

It develops Markov chain algorithms for the 1-2 model and establishes polynomial mixing time bounds for a broad class of measures.

## Key findings

- Mixing time is polynomial in graph size.
- Markov chains effectively sample 1-2 model configurations.
- Applicable to a large class of probability measures.

## Abstract

A 1-2 model configuration is a subset of edges of a hexagonal lattice satisfying the constraint that each vertex is incident to 1 or 2 edges. We introduce Markov chains to sample the 1-2 model configurations on 2D hexagonal lattice and prove that the mixing time of these chains is polynomial in the sizes of the graphs for a large class of probability measures.