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Glassy phase and freezing of log-correlated Gaussian potentials

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Date
2016
Publisher city
Paris
Link to item file
https://arxiv.org/abs/1310.5574v1
Dewey
Probabilités et mathématiques appliquées
Sujet
glassy phase; derivative multiplicative chaos; freezing; renormalization; supercritical; Gaussian multiplicative chaos
Journal issue
The Annals of Applied Probability
Volume
26
Number
2
Publication date
2016
Article pages
643-690
Publisher
Institute of Mathematical Statistics
DOI
http://dx.doi.org/10.1214/14-AAP1071
URI
https://basepub.dauphine.fr/handle/123456789/12272
Collections
  • CEREMADE : Publications
Metadata
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Author
Madaule, Thomas
Rhodes, Rémi
Vargas, Vincent
Type
Article accepté pour publication ou publié
Abstract (EN)
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.

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