Hierarchical exchangeability of pure states in mean field spin glass models

• 成果类型: Article
• 署名作者: Panchenko, Dmitry
• 署名单位: Texas A&M University System; Texas A&M University College Station
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-014-0555-y
• 发表日期: 2015
• 页码: 619-650
• 关键词: ghirlanda-guerra identities; parisi ultrametricity; systems; bounds; distributions; arrays

摘要

The main result in this paper is motivated by the M,zard-Parisi ansatz which predicts a very special structure for the distribution of spins in diluted mean field spin glass models, such as the random -sat model at positive temperature. Using the fact that one can safely assume the validity of the Ghirlanda-Guerra identities in these models, we prove hierarchical exchangeability of pure states for the asymptotic Gibbs measures, which allows us to apply a representation result for hierarchically exchangeable arrays recently proved in Austin and Panchenko in Probab. Theory Relat. Fields 2013. Comparing this representation with the predictions of the M,zard-Parisi ansatz, one can see that the key property still missing is that the multi-overlaps between pure states depend only on their overlaps.