## The Annals of Applied Probability

### Glassy phase and freezing of log-correlated Gaussian potentials

#### Abstract

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.

#### Article information

Source
Ann. Appl. Probab., Volume 26, Number 2 (2016), 643-690.

Dates
Revised: September 2014
First available in Project Euclid: 22 March 2016

https://projecteuclid.org/euclid.aoap/1458651816

Digital Object Identifier
doi:10.1214/14-AAP1071

Mathematical Reviews number (MathSciNet)
MR3476621

Zentralblatt MATH identifier
1341.60094

Subjects
Primary: 60G57: Random measures 60G15: Gaussian processes

#### Citation

Madaule, Thomas; Rhodes, Rémi; Vargas, Vincent. Glassy phase and freezing of log-correlated Gaussian potentials. Ann. Appl. Probab. 26 (2016), no. 2, 643--690. doi:10.1214/14-AAP1071. https://projecteuclid.org/euclid.aoap/1458651816

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