Glassy phase and freezing of log-correlated Gaussian potentials

Thomas Madaule (1) , Rémi Rhodes (2) , Vincent Vargas (3)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 DMA - Département de Mathématiques et Applications - ENS Paris

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 renormalization theory of super-critical Gaussian multiplicative chaos.

Mots clés: Gaussian multiplicative chaos; supercritical; renormalization; freezing; glassy phase; derivative multiplicative chaos

Domaines: Probabilités [math.PR]

Thomas Madaule, Rémi Rhodes, Vincent Vargas. Glassy phase and freezing of log-correlated Gaussian potentials. The Annals of Applied Probability, 2016, 26 (2). ⟨hal-00914384⟩