Skip to main content

Research Repository

Advanced Search

Correlation decay for hard spheres via Markov chains

Helmuth, Tyler; Perkins, Will; Petti, Tyler

Correlation decay for hard spheres via Markov chains Thumbnail


Will Perkins

Tyler Petti


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.


Helmuth, T., Perkins, W., & Petti, T. (2022). Correlation decay for hard spheres via Markov chains. Annals of Applied Probability, 32(3), 2063-2082.

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
Related Public URLs


You might also like

Downloadable Citations