A 1-2 model configuration is a subgraph of the hexagonal lattice satisfying the constraint that each vertex is incident to 1 or 2 edges in the subgraph. We introduce Markov chains to sample the 1-2 model configurations on finite hexagonal graphs under the uniform probability measure, and prove that the mixing time of these chains is polynomial in the size of the graphs.
Averaging over fast variables in the fluid limit for Markov chains: Application to the supermarket model with memory
Comparison Theory for Markov Chains on Different State Spaces and Application to Random Walk on Derangements
Commutation relations and Markov chains
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