Glassy phase and freezing of log-correlated Gaussian potentials

@article{Madaule2013GlassyPA,
  title={Glassy phase and freezing of log-correlated Gaussian potentials},
  author={Thomas Madaule and R{\'e}mi Rhodes and Vincent Vargas},
  journal={Annals of Applied Probability},
  year={2013},
  volume={26},
  pages={643-690}
}
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 \cite{Rnew7,Rnew12}. This could be seen as a first rigorous step in the… 

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