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April 2016 Glassy phase and freezing of log-correlated Gaussian potentials
Thomas Madaule, Rémi Rhodes, Vincent Vargas
Ann. Appl. Probab. 26(2): 643-690 (April 2016). DOI: 10.1214/14-AAP1071


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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Thomas Madaule. Rémi Rhodes. Vincent Vargas. "Glassy phase and freezing of log-correlated Gaussian potentials." Ann. Appl. Probab. 26 (2) 643 - 690, April 2016.


Received: 1 May 2014; Revised: 1 September 2014; Published: April 2016
First available in Project Euclid: 22 March 2016

zbMATH: 1341.60094
MathSciNet: MR3476621
Digital Object Identifier: 10.1214/14-AAP1071

Primary: 60G15, 60G57

Rights: Copyright © 2016 Institute of Mathematical Statistics


Vol.26 • No. 2 • April 2016
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