Correlation decay for hard spheres via Markov chains

Helmuth, Tyler; Perkins, Will; Petti, Tyler

doi:10.1214/21-aap1728

Correlation decay for hard spheres via Markov chains

Helmuth, Tyler; Perkins, Will; Petti, Tyler

Authors

Dr Tyler Helmuth tyler.helmuth@durham.ac.uk
Associate Professor

Will Perkins

Tyler Petti

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
Related Public URLs	https://arxiv.org/abs/2001.05323