GLASSY PHASE AND FREEZING OF LOG-CORRELATED GAUSSIAN POTENTIALS

• 成果类型: Article
• 署名作者: Madaule, Thomas; Rhodes, Remi; Vargas, Vincent
• 署名单位: Universite Paris 13; Universite PSL; Universite Paris-Dauphine; Universite PSL; Ecole Normale Superieure (ENS)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/14-AAP1071
• 发表日期: 2016
• 页码: 643-690
• 关键词: multiplicative chaos

摘要

In this paper, we consider the Gibbs measure associated to a logarithmically correlated random potential (including two-dimensional free fields) at low temperature. We prove that the energy landscape freezes and enters in the so-called glassy phase. The limiting Gibbs weights are integrated atomic random measures with random intensity expressed in terms of the critical Gaussian multiplicative chaos constructed in [Ann. Probab. 42 (2014) 1769-1808 and Comm. Math. Phys. (2013) To appear]. This could be seen as a first rigorous step in the renormalization theory of super-critical Gaussian multiplicative chaos.