Helmuth, Tyler and Perkins, Will and Petti, Tyler (2022) 'Correlation decay for hard spheres via Markov chains.', Annals of Applied Probability, 32 (3). pp. 2063-2082.
We improve upon all known lower bounds on the critical fugacity and critical density of the hard sphere model in dimensions three 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 temporal mixing for hard spheres to deduce our results.
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|Publisher Web site:||https://doi.org/10.1214/21-AAP1728|
|Date accepted:||16 July 2021|
|Date deposited:||19 July 2022|
|Date of first online publication:||29 May 2022|
|Date first made open access:||19 July 2022|
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