Journal
ANNALS OF APPLIED PROBABILITY
Volume 26, Issue 2, Pages 643-690Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/14-AAP1071
Keywords
Gaussian multiplicative chaos; supercritical; renormalization; freezing; glassy phase
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Funding
- ANR-11-JCJC CHAMU
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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.
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