Correlation decay for hard spheres via Markov chains

Helmuth, Tyler; Perkins, Will; Petti, Tyler

Abstract

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.

Citation

Helmuth, T., Perkins, W., & Petti, T. (2022). Correlation decay for hard spheres via Markov chains. Annals of Applied Probability, 32(3), 2063-2082. https://doi.org/10.1214/21-aap1728

• Journal Article Type: Article
• Acceptance Date: Jul 16, 2021
• Online Publication Date: May 29, 2022
• Publication Date: 2022-06
• Deposit Date: Jul 21, 2021
• Publicly Available Date: Jul 19, 2022
• Journal: Annals of Applied Probability
• Print ISSN: 1050-5164
• Publisher: Institute of Mathematical Statistics
• Peer Reviewed: Peer Reviewed
• Volume: 32
• Issue: 3
• Pages: 2063-2082
• DOI: https://doi.org/10.1214/21-aap1728
• Public URL: https://durham-repository.worktribe.com/output/1239235
• Related Public URLs: https://arxiv.org/abs/2001.05323