CORRELATION DECAY FOR HARD SPHERES VIA MARKOV CHAINS

• 成果类型: Article
• 署名作者: Helmuth, Tyler; Perkins, Will; Petti, Samantha
• 署名单位: Durham University; University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; Harvard University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/21-AAP1728
• 发表日期: 2022
• 页码: 2063-2082
• 关键词: spectral gap; spin systems; uniqueness; DYNAMICS; square

摘要

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.