Correlation decay for hard spheres via Markov chains

@article{Helmuth2022CorrelationDF,
  title={Correlation decay for hard spheres via Markov chains},
  author={Tyler Helmuth and Will Perkins and Samantha Petti},
  journal={ArXiv},
  year={2022},
  volume={abs/2001.05323}
}
We improve upon all known lower bounds on the critical fugacity and critical density of the hard sphere model in dimensions two and higher. As the dimension tends to infinity our improvements are by factors of $2$ and $1.7$, respectively. We make these improvements by utilizing techniques from theoretical computer science to show that a certain Markov chain for sampling from the hard sphere model mixes rapidly at low enough fugacities. We then prove an equivalence between optimal spatial and… 
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