A representation of Gibbs measure for the random energy model

• 成果类型: Article
• 署名作者: Kratz, MF; Picco, P
• 署名单位: Universite Paris Cite; Aix-Marseille Universite
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051604000000053
• 发表日期: 2004
• 页码: 651-677
• 关键词: sherrington-kirkpatrick model; spin-glass model; solvable model; iid sequence; rem; thermodynamics; fluctuations; CHALLENGE; EXISTENCE; Spacings

摘要

In this work we consider a problem related to the equilibrium statistical mechanics of spin glasses, namely the study of the Gibbs measure of the random energy model. For solving this problem, new results of independent interest on sums of spacings for i.i.d. Gaussian random variables are presented. Then we give a precise description of the support of the Gibbs measure below the critical temperature.