LOCALIZATION IN GAUSSIAN DISORDERED SYSTEMS AT LOW TEMPERATURE

• 成果类型: Article
• 署名作者: Bates, Erik; Chatterjee, Sourav
• 署名单位: University of California System; University of California Berkeley; Stanford University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/20-AOP1436
• 发表日期: 2020
• 页码: 2755-2806
• 关键词: random-energy model; spin-glass; directed polymers; random environment; path localization; solvable model; ultrametricity; limit

摘要

For a broad class of Gaussian disordered systems at low temperature, we show that the Gibbs measure is asymptotically localized in small neighborhoods of a small number of states. From a single argument, we obtain: (i) a version of complete path localization for directed polymers that is not available even for exactly solvable models, and (ii) a result about the exhaustiveness of Gibbs states in spin glasses not requiring the Ghirlanda-Guerra identities.