The spectral gap of the REM under metropolis dynamics

• 成果类型: Article
• 署名作者: Fontes, LRG; Isopi, M; Kohayakawa, Y; Picco, P
• 署名单位: Universidade de Sao Paulo; Sapienza University Rome; Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 1998
• 页码: 917-943
• 关键词: random-energy-model; random spin systems; disordered-systems; equilibrium; decay

摘要

We derive upper and lower bounds for the spectral gap of the random energy model under Metropolis dynamics which are sharp in exponential order. They are based on the Variational characterization of the gap. For the lower bound, a Poincare inequality derived by Diaconis and Stroock is used. The scaled asymptotic expression is a linear function of the temperature. The corresponding function for a global version of the dynamics exhibits phase transition instead. We also study the dependence of lower order terms on the volume. In the global dynamics, we observe a phase transition. For the local dynamics, the expressions we have, which are possibly not sharp, do not change their order of dependence on the volume as the temperature changes.